Deck 13: Simple Linear Regression

Question 1

TABLE 13-10
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | l | l | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Table 13-10, which is the correct null hypothesis for testing whether the number of customers who make purchase affects weekly sales?

A) H₀ : ?₀ = 0
B) H₀ : µ = 0
C) H₀ : ?₁ = 0
D) H₀ : ?= 0

Answer 1

H₀ : ?₁ = 0

Question 2

TABLE 13-7
An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following EXCEL output.
$$\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Error } &T \text { Stat } & \text { p-value } \\\hline \text { Intercept } & 4.866004258 & 0.35743609 & 13.61363441 & 8.7932 \mathrm { E } - 13 \\\text { S\& P } & - 0.502513506 & 0.071597152 & - 7.01862425 & 294942 \mathrm { E } - 07 \\\hline\end{array}$$

-Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the measured value of the test statistic is

A) 0.357.
B) 0.072.
C) -0.503.
D) -7.019.

Answer 2

-7.019.

Question 3

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is $?(X -\bar X )^2$ for these data?

A) 2.54
B) 0
C) 1.66
D) 25.66

Answer 3

1.66

Question 4

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is the coefficient of correlation for these data?

A) - 0.7839
B) 0.8854
C) 0.7839
D) - 0.8854

Question 5

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$\begin{array}{lc}\text { Regression Statistics } \\\hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { Observations } & 30\end{array}$


$\text { ANOVA }$
$\begin{array}{lccccc} & d f & \text { SS } & \text { MS } & F & \text { Significance } F \\\text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\\text { Residual } & 28 & 3.1282 & 0.1117 & & \\\text { Total } & 29 & 29.072 & & \\\hline\end{array}$


$\begin{array}{lrrrrrr}\hline & \text { Coeffcients } & \text { StandardError } & t \text { Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Invoices } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\\text { Processed } & 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \\\hline\end{array}$


-Referring to Table 13-12, the degrees of freedom for the F test on whether the number of invoices processed affects the amount of time are

A) 1, 29.
B) 28, 1.
C) 29, 1.
D) 1, 28.

Question 6

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-The sample correlation coefficient between X and Y is 0.375. It has been found out that the p- value is 0.744 when testing H0 : ? = 0 against the one- sided alternative H0 : ? < 0. To test H0 : ? = 0 against the two- sided alternative H0 : ?? 0 at a significance level of 0.2, the p- value is

A) (1 - 0.744)(2).
B) (0.744)(2).
C) 0.744/2.
D) 1 - 0.744.

Question 7

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8857 \\\text { R Square } & 0.7845 \\\text { Adjusted R Square } & 0.7801 \\\text { Standard Error } & 1.3704 \\\text { Observations } & 51 \\\hline\end{array}\end{array}$$
$\text { ANOVA }$
$\begin{array}{llcc}\hline&\text { df }&\text { SS } &\text { MS }&\text {F }&\text { Significance F } \\\text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & & 1.8782 & \\\text { Total } & 50 & 427.0798 & &\end{array}$

-Referring to Table 13-9, the 90% confidence interval for the average change in SALARY (in thousands of dollars) as a result of spending an extra hour per day studying is

A) wider than [-2.70159, -1.08654].
B) wider than [0.8321927, 1.12697].
C) narrower than [0.8321927, 1.12697].
D) narrower than [-2.70159, -1.08654].

Question 8

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

A) The variance of the distribution increases as X increases.
B) The distribution is normal.
C) The errors are independent.
D) The mean of the distribution is 0.

Question 9

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8857 \\\text { R Square } & 0.7845 \\\text { Adjusted R Square } & 0.7801 \\\text { Standard Error } & 1.3704 \\\text { Observations } & 51 \\\hline\end{array}\end{array}$$
$\text { ANOVA }$
$\begin{array}{llcc}\hline&\text { df }&\text { SS } &\text { MS }&\text {F }&\text { Significance F } \\\text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & & 1.8782 & \\\text { Total } & 50 & 427.0798 & &\end{array}$

-Referring to Table 13-9, the value of the measured t-test statistic to test whether average SALARY depends linearly on HOURS is $$\begin{array} { l r c c c r r } & \text { Coefficients } & \text { Standaad Error } &t \text { Stat } & p \text {-value } & \text { Lower 95\%} & \text { Upper 95\% } \\\hline \text { Intercept } & - 1.8940 & 0.4018 & - 4.7134 & 2.051 \mathrm { E } - 05 & - 2.7015 & - 1.0865 \\\text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm { E } - 18 & 0.8321 & 1.1269 \\\hline\end{array}$$

A) 13.3561.
B) 0.9795.
C) -4.7134.
D) -1.8940.

Question 10

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is the percentage of the total variation in candy bar sales explained by the regression model?

A) 78.39%
B) 100%
C) 48.19%
D) 88.54%

Question 11

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
$\begin{array}{lc}\text { Regression Statistics } & \\\hline \text { Multiple R } & 0.8857 \\\text { R Square } & 0.7845 \\\text { Adjusted R Square } & 0.7801 \\\text { Standard Error } & 1.3704 \\\text { Observations } & 51\end{array}$
$\text { ANOVA }$
$\begin{array}{llcc}\hline&\text { df }&\text { SS } &\text { MS }&\text {F }&\text { Significance F } \\\text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & & 1.8782 & \\\text { Total } & 50 & 427.0798 & &\end{array}$

-Referring to Table 13-9, the degrees of freedom for the F test on whether HOURS affects SALARY are $$\begin{array} { l r c c c r r } & \text { Coefficients } & \text { Standaad Error } &t \text { Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & - 1.8940 & 0.4018 & - 4.7134 & 2.051 \mathrm { E } - 05 & - 2.7015 & - 1.0865 \\\text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm { E } - 18 & 0.8321 & 1.1269 \\\hline\end{array}$$

A) 50, 1.
B) 1, 50.
C) 49, 1.
D) 1, 49.

Question 12

If you wanted to find out if alcohol consumption (measured in fluid oz.) and grade point average on a 4-point scale are linearly related, you would perform a

A) a t test for a correlation coefficient.
B) ?² test for independence.
C) ?² test for the difference in two proportions.
D) a Z test for the difference in two proportions.

Question 13

Testing for the existence of correlation is equivalent to

A) the confidence interval estimate for predicting Y.
B) testing for the existence of the slope (?₁).
C) testing for the existence of the Y-intercept (?₂).
D) none of the above

Question 14

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
$\begin{array}{lc}\text { Regression Statistics } & \\\hline \text { Multiple R } & 0.8857 \\\text { R Square } & 0.7845 \\\text { Adjusted R Square } & 0.7801 \\\text { Standard Error } & 1.3704 \\\text { Observations } & 51\end{array}$
$\text { ANOVA }$
$\begin{array}{llcc}\hline&\text { df }&\text { SS } &\text { MS }&\text {F }&\text { Significance F } \\\text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & & 1.8782 & \\\text { Total } & 50 & 427.0798 & &\end{array}$

-Referring to Table 13-9, the estimated average change in salary (in thousands of dollars) as a result of spending an extra hour per day studying is

A) 0.9795.
B) -1.8940.
C) 0.7845.
D) 335.0473.

Question 15

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array} { l c } { \text { Regression } \text { Statistics } } \\\hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { Observations } & 30 \\\hline\end{array}$$ $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Significance } F \\\text { Regression } & 1 & 25.9438&25 .9438 & 232.2200&4 .3946 \mathrm { E } - 15 \\\text { Residual } & 28 & 3.12820 .1117 & \\\text { Total } & 29 & 29.072 \\\hline\end{array}\end{array}$$ $$\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Enror } & t \text { Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Invoices } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\\text { Processed } & 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm { E } 15 & 0.0109 & 0.0143\end{array}$$ $\begin{array}{rrrrrrr} & \text { Coefficients } & \text { Standard Enor } & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Invoices } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555\end{array}$


-Referring to Table 13-12, the 90% confidence interval for the average change in the amount of time needed as a result of processing one additional invoice is

A) narrower than [0.0109, 0.0143].
B) wider than [0.0109, 0.0143].
C) narrower than [0.1492, 0.6555].
D) wider than [0.1492, 0.6555].

Question 16

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, if the price of the candy bar is set at $2, the estimated average sales will be

A) 30.
B) 90.
C) 100.
D) 65.

Question 17

What do we mean when we say that a simple linear regression model is "statistically" useful?

A) The model is an excellent predictor of Y.
B) The model is a better predictor of Y than the sample mean, Y.
C) The model is "practically" useful for predicting Y.
D) All the statistics computed from the sample make sense.

Question 18

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p- value is 0.256 when testing H₀ : q = 0 against the one- sided alternative H₀ : q > 0. To test H₀ : q = 0 against the two- sided alternative H₀ : q × 0 at a significance level of 0.2, the p- value is

A) (0.256)(2).
B) 1 - 0.256/2.
C) 0.256/2.
D) 1 - 0.256.

Question 19

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array} { l c } { \text { Regression } \text { Statistics } } \\\hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { Observations } & 30 \\\hline\end{array}$$ $\text{ANOVA}$

$\begin{array}{llcc}&\text { df} &\text {SS } &\text {M S}&\text { F}&\text { Significance F}\\\text { Regression } &1&25.9438&25 .9438&232 .2200&4 .3946 \mathrm{E}-15\\\text {Residual }&28 &3.12820 .1117 \\\text { Total } & 29 & 29.072\end{array}$



-Referring to Table 13-12, the degrees of freedom for the t test on whether the number of invoices processed affects the amount of time are

A) 1.
B) 28.
C) 30.
D) 29.

Question 20

The least squares method minimizes which of the following?

A) SSR
B) SST
C) SSE
D) all of the above

Question 21

TABLE 13-5
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data with the following results:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.802 \\\text { R Square } & 0.643 \\\text { Adjusted R Square } & 0.618 \\\text { Standard Error } S Y X & 0.9224 \\\text { Observations } & 16 \\\hline\end{array}\end{array}$$ $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l r l r l r } \hline & d f & \text { SS } & \text { MS } & F & \text { Sig. } F \\\hline \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\\text { Error } & 14 & 11.912 & 0.851 & & \\\text { Total } & 15 & 33.409 & & &\end{array}\end{array}$$ $$\begin{array}{l}\text { Predictor }&\text { Coefficients}&\text { Standard Error }& t \text { Stat } &p \text {-value }\\\text { Intercept } & 3.962 & 1.440 & 2.75 & 0.016\\\text { Industry } & 0.040451 & 0.008048 & 5.03 & 0.000\end{array}$$ Durbin- Watson Statistic 1.59

-Referring to Table 13-5, the partner wants to test for autocorrelation using the Durbin-Watson statistic. Using a level of significance of 0.05, the decision he should make is

A) there is no evidence of autocorrelation.
B) there is not enough information to perform the test.
C) there is evidence of autocorrelation.
D) the test is unable to make a definite conclusion.

Question 22

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, to test whether a change in price will have any impact on average sales, what would be the critical values? Use ? = 0.05.

A) ±2.7765
B) ±2.5706
C) ±3.1634
D) ±3.4954

Question 23

If the correlation coefficient (r) = 1.00, then

A) there is no explained variation.
B) there is no unexplained variation.
C) the Y-intercept (b0) must equal 0.
D) the explained variation equals the unexplained variation.

Question 24

If the plot of the residuals is fan shaped, which assumption is violated?

A) independence of errors
B) normality
C) homoscedasticity
D) No assumptions are violated; the graph should resemble a fan.

Question 25

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { ations } & 30 \\\hline\end{array}\end{array}$$

$\begin{array}{lrrccc}\hline & \text { d f } & \text { SS } & \text {MS} & \text { F } & \text { Significance F } \\\hline \text {Regression} & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text {Residual }& 28 & 3.1282 & 0.1117 & & \\ \text {Total }& 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text { Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value}& \text {Lower 95\%} & \text {Upper 95\%} \\\hline \text { Invoices }& 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text {Processed }& 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \\\hline\end{array}$






-Referring to Table 13-12, the p-value of the measured t-test statistic to test whether the number of invoices processed affects the amount of time is

A) (0.0030)/2.
B) 0.0030.
C) 4.3946E-15.
D) (4.3946E-15)/2.

Question 26

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals - 0.30,

A) the slope (b₁) is negative.
B) there is no correlation.
C) variable X is larger than variable Y.
D) the variance of X is negative.

Question 27

TABLE 13-01
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
$E(Y)=\beta_{0}+\beta_{1} X$
The results of the simple linear regression are provided below.
$\hat{Y}=-2,700+20 X, \mathrm{~S}_{Y X}=65, \text { two-tailed } p \text { value }=0.034\left(\text { for testing } \beta_{1}\right)$


-Referring to Table 13-1, interpret the p-value for testing whether þ1 exceeds 0.

A) There is sufficient evidence (at the ? = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
B) For every $1 million increase in sales revenue, we expect a service charge to increase $0.034.
C) There is insufficient evidence (at the ? = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
D) Sales revenue (X) is a poor predictor of service charge (Y).

Question 28

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what percentage of the total variation in candy bar sales is explained by prices?

A) 100%
B) 78.39%
C) 88.54%
D) 48.19%

Question 29

The Y-intercept (b₀) represents the

A) change in estimated average Y per unit change in X.
B) variation around the sample regression line.
C) predicted value of Y.
D) estimated average Y when X = 0.

Question 30

TABLE 13- 11
A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8531 \\\text { RSquare } & 0.7278 \\\text { Adjusted R Square } & 0.7180 \\\text { Standard Error } & 47.8668 \\\text { Observations } & 30\end{array}\end{array}$$
ANOVA
$\begin{array}{lrrrrr}\hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\\hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\\text {Residual} & 28 & 64154.42 & 2291.23 & & \\\text {Total} & 29 & 235654.20 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\\hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\\hline\end{array}$



-Referring to Table 13-11, which of the following is the correct interpretation for the slope coefficient?

A) For each increase of 1 dollar in box office gross, expected home video units sold are estimated to increase by 4.3331 thousand units.
B) For each increase of 1 million dollars in box office gross, expected home video units sold are estimated to increase by 4.3331 units.
C) For each increase of 1 dollar in box office gross, expected home video units sold are estimated to increase by 4.3331 units.
D) For each increase of 1 million dollars in box office gross, expected home video units sold are estimated to increase by 4.3331 thousand units.

Question 31

TABLE 13-01
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges
$E(Y)=\beta_{0}+\beta_{1} X$
The results of the simple linear regression are provided below.
$\hat{Y}=-2,700+20 X, \mathrm{~S}_{Y X}=65, \text { two-tailed } p \text { value }=0.034\left(\text { for testing } \beta_{1}\right)$

(Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:



-Referring to Table 13-1, interpret the estimate of a, the standard deviation of the random error term (standard error of the estimate) in the model.

A) About 95% of the observed service charges fall within $130 of the least squares line.
B) For every $1 million increase in sales revenue, we expect a service charge to increase $65.
C) About 95% of the observed service charges fall within $65 of the least squares line.
D) About 95% of the observed service charges equal their corresponding predicted values.

Question 32

TABLE 13-01
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
E(Y) =?₀ + ?₁X
The results of the simple linear regression are provided below.

$\hat{Y}=-2,700+20 X, S_{Y X}=65$ , two-tailed $p$ value $=0.034\left(\right.$ for testing $\left.\beta_{1}\right)$


-Referring to Table 13-1, a 95% confidence interval for ?₁ is (15, 30). Interpret the interval.

A) At the ? = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).
B) We are 95% confident that the mean service charge will fall between $15 and $30 per month.
C) We are 95% confident that average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X).
D) We are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y).

Question 33

The slope (b₁) represents

A) the estimated average change in Y per unit change in X.
B) predicted value of Y when X = 0.
C) the predicted value of Y.
D) variation around the line of regression.

Question 34

TABLE 13-7
An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following EXCEL output.
$$\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Enor } & \text { T Stat } & p \text {-value } \\\hline \text { Intercept } & 4.866004258 & 0.35743609 & 13.61363441 & 8.7932 \mathrm { E } - 13 \\\text { S\&P } & - 0.502513506 & 0.071597152 -& 7.01862425 & 2.94942 \mathrm { E } - 07 \\\hline\end{array}$$

-Referring to Table 13-7, which of the following will be a correct conclusion?

A) We can reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related.
B) We can reject the null hypothesis and conclude that there is not sufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related.
C) We cannot reject the null hypothesis and, therefore, conclude that there is not sufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related.
D) We cannot reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related.

Question 35

$$\text { TABLE 13-10 }$$ The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | c | c | } \hline \text { Cugtomera } & \text { 5aleg (Thougardaof Dollara) } \\\hline \mathbf { 9 0 7 } & 11.20 \\\hline \mathbf { 9 2 6 } & 11.05 \\\hline 713 & \mathbf { 8 . 2 1 } \\\hline 741 & \mathbf { 9 . 2 1 } \\\hline 780 & \mathbf { 9 . 4 2 } \\\hline \mathbf { 8 9 8 } & \mathbf { 1 0 . 0 8 } \\\hline 510 & \mathbf { 6 . 7 3 } \\\hline 529 & 7.02 \\\hline 460 & \mathbf { 6 . 1 2 } \\\hline \mathbf { 8 7 2 } & \mathbf { 9 . 5 2 } \\\hline \mathbf { 6 5 0 } & 7.53 \\\hline \mathbf { 6 0 3 } & 7.25 \\\hline\end{array}$$

-Referring to Table 13-10, the residual plot indicates possible violation of which assumptions?

A) normality
B) autocorrelation
C) linearity of the relationship
D) homoscedasticity

Question 36

In a simple linear regression problem, r and b₁

A) must have the same sign.
B) may have opposite signs.
C) must have opposite signs.
D) are equal.

Question 37

The standard error of the estimate is a measure of

A) the variation of the X variable.
B) total variation of the Y variable.
C) the variation around the sample regression line.
D) explained variation.

Question 38

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
$\begin{array}{ll}\text { Regression Stedistics } \\\hline \text { Multiple R } & 0.8857 \\\text { RSquare } & 0.7845 \\\text { Adjusted R Square } & 0.7801 \\\text { Standard Error } & 1.3704\end{array}$

$\text { Observations } \quad 51$

$ANOVA$
$\begin{array}{lccrcc}\hline & d f & S S &{M S} & F & \text { Significance } F \\\hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & 1.8782 & \\\text { Total } & 50 & 427.0798 & & \\\hline\end{array}$


$\begin{array}{lccccrr}\hline & \text { Coeffcients } & \text { Standard Error }& t \text { Stat } & p \text {-value } & \text { Lower 95\%} & \text { Upper 95\% } \\\hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 2.051 \mathrm{E}-05 & -2.7015 & -1.0865 \\\text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm{E}-18 & 0.8321 & 1.1269 \\\hline\end{array}$



-Referring to Table 13-9, to test the claim that average SALARY depends positively on HOURS against the null hypothesis that average SALARY does not depend linearly on HOURS, the p-value of the test statistic is

A) (2.051E-05)/2.
B) 5.944E-18.
C) (5.944E-18)/2.
D) 2.051E-05.

Question 39

The strength of the linear relationship between two numerical variables may be measured by the

A) slope.
B) Y-intercept.
C) coefficient of correlation.
D) scatter diagram.

Question 40

TABLE 13-8
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
$$\begin{array}{l}\text { Regressing GPA on } \mathrm { ACT }\\\begin{array} { l c } \hline & \text { Regression Statistics } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard E rror } & 0.2691 \\\text { Observations } & 8\end{array}\end{array}$$

ANOVA
$\begin{array}{lcllcc}\hline & \text {d f} & \text {SS} & \text { MS }& \text { F } & \text { Significance F} \\\hline \text {Regression }&1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\ \text {Residual }& 6 & 0.4347 & 0.0724 & & \\ \text {Total }& 7 & 1.0287 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text {Standard Error }& \text {T Stat }& \text { p -value }& \text {Lower 95\%}& \text { Upper 95\% } \\\hline \text { Intercept} & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\ \text {ACT }& 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$


-Referring to Table 13-8, the value of the measured (observed) test statistic of the F-test for H0 : ?₁ = 0 versus H₁ : ?₁ ? 0

A) is always positive.
B) has the same sign as the corresponding t test statistic.
C) may be negative.
D) is always negative.

Question 41

The coefficient of determination (r²) tells us

A) the proportion of total variation that is explained.
B) that we should not partition the total variation.
C) whether r has any significance.
D) that the coefficient of correlation (r) is larger than 1.

Question 42

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
$$\begin{array}{l}\text { Regression Stedistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8857 \\\text { R Square } & 0.7845 \\ \text { Adjusted R Square } & 0.7801 \\\text { Standard Error } & 1.3704 \\\text { Observations } & 51\end{array}\end{array}$$ $\text { ANOVA }$
$\begin{array}{lccrcc}\hline & d f & S S &{M S} & F & \text { Significance } F \\\hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & & 1.8782 & \\\text { Total } & 50 & 427.0798 & &\end{array}$ $$\begin{array} { l r c c c r r } & \text { Coefficients } & \text { Standard Enror } & t \text { Stat } & { p \text {-value } } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & - 1.8940 & 0.4018 & - 4.7134 & 2.051 \mathrm { E } - 05 & - 2.7015 & - 1.0865 \\\text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm { E } - 18 & 0.8321 & 1.1269 \\\hline\end{array}$$ $$\begin{array} { l r r r r r r } \end{array}$$

-Referring to Table 13-9, the error sum of squares (SSE) of the above regression is

A) 1.878215.
B) 335.047257.
C) 92.0325465.
D) 427.079804.

Question 43

TABLE 13-7
An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following EXCEL output.
$$\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Error } & \text { T Stat } & { p \text {-value } } \\\hline \text { Intercept } & 4.866004258 & 0.35743609 & 13.61363441 & 8.7932 \mathrm { E } - 13 \\\text { S\& P } & - 0.502513506 & 0.071597152 &- 7.01862425 & 294942 \mathrm { E } - 07 \\\hline\end{array}$$

-Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the p-value of the associated test statistic is

A) 8.7932E- 13.
B) 2.94942E- 07.
C) (2.94942E- 07)2.
D) 2.94942E- 07/2.

Question 44

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is the standard error of the regression slope estimate, S_b1?

A) 12.650
B) 0.784
C) 0.885
D) 16.299

Question 45

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is the standard error of the estimate, SYX, for the data?

A) 0.885
B) 16.299
C) 0.784
D) 12.650

Question 46

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H₀ : ? = 0 against the two-sided alternative H₀ :? ? 0. To test H₀ : ? = 0 against the one-sided alternative H₀ : ? < 0 at a significance level of 0.2, the p-value is

A) 1 - 0.256/2.
B) (0.256)2.
C) 1 - 0.256.
D) 0.256/2.

Question 47

The width of the prediction interval for the predicted value of Y is dependent on

A) the standard error of the estimate.
B) the sample size.
C) the value of X for which the prediction is being made.
D) all of the above

Question 48

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p- value is 0.256 when testing H₀ : ? = 0 against the two- sided alternative H₀: ?? 0. To test H₀ :? = 0 against the one- sided alternative H0 : ? > 0 at a significance level of 0.2, the p- value is

A) (0.256)2.
B) 1 - 0.256/2.
C) 0.256/2.
D) 1 - 0.256.

Question 49

Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions?

A) Homoscedasticity
B) Independence of errors
C) Normality of errors
D) Linearity of the relationship

Question 50

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { ations } & 30 \\\hline\end{array}\end{array}$$

$\begin{array}{lrrccc}\hline & \text { d f } & \text { SS } & \text {MS} & \text { F } & \text { Significance F } \\\hline \text {Regression} & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text {Residual }& 28 & 3.1282 & 0.1117 & & \\ \text {Total }& 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text { Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value}& \text {Lower 95\%} & \text {Upper 95\%} \\\hline \text { Invoices }& 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text {Processed }& 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \\\hline\end{array}$






-Referring to Table 13-12, the p-value of the measured F-test statistic to test whether the number of invoices processed affects the amount of time is

A) (4.3946E-15)/2.
B) (0.0030)/2.
C) 0.0030.
D) 4.3946E-15.

Question 51

If the correlation coefficient (r) = 1.00, then

A) all the data points must fall exactly on a straight line with a slope that equals 1.00.
B) all the data points must fall exactly on a straight line with a negative slope.
C) all the data points must fall exactly on a horizontal straight line with a zero slope.
D) all the data points must fall exactly on a straight line with a positive slope.

Question 52

TABLE 13- 11
A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8531 \\\text { RSquare } & 0.7278 \\\text { Adjusted R Square } & 0.7180 \\\text { Standard Error } & 47.8668 \\\text { Observations } & 30\end{array}\end{array}$$
ANOVA
$\begin{array}{lrrrrr}\hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\\hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\\text {Residual} & 28 & 64154.42 & 2291.23 & & \\\text {Total} & 29 & 235654.20 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\\hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\\hline\end{array}$



-Referring to Table 13-11, which of the following assumptions appears to have been violated?

A) homoscedasticity
B) independence of errors
C) normality of error
D) none of the above

Question 53

TABLE 13-8
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
$\text {Regressing GPA on \(\mathrm { ACT }\)}$
$$\begin{array}{l}\text { Regressing GPA on } \mathrm { ACT }\\\begin{array} { l c } \hline & \text { Regression Statistics } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard E rror } & 0.2691 \\\text { Observations } & 8\end{array}\end{array}$$

ANOVA
$\begin{array}{lcllcc}\hline & \text {d f} & \text {SS} & \text { MS }& \text { F } & \text { Significance F} \\\hline \text {Regression }&1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\ \text {Residual }& 6 & 0.4347 & 0.0724 & & \\ \text {Total }& 7 & 1.0287 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text {Standard Error }& \text {T Stat }& \text { p -value }& \text {Lower 95\%}& \text { Upper 95\% } \\\hline \text { Intercept} & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\ \text {ACT }& 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$



-Referring to Table 13-8, the interpretation of the coefficient of determination in this regression is

A) ACT scores account for 57.74% of the total fluctuation in GPA.
B) 57.74% of the total variation of ACT scores can be explained by GPA.
C) GPA accounts for 57.74% of the variability of ACT scores.
D) none of the above

Question 54

TABLE 13-6
The following EXCEL tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.
$\begin{array}{lc}\text { Regression Statistics } \\\text { Multiple R } & 0.142620229 \\\text { R Square } & 0.02034053 \\\text { Adjusted R Square } & -0.028642444 \\\text { Standard Error} &20.25979924 \\\text { Observations } & 22 \\\hline\end{array}$

$$\begin{array} { l c r c c } \hline & \text { Coefficients } & \text { Standard Enor } & \text { T Stat } & p \text {-value } \\\hline \text { Intercept } & 39.39027309 & 37.24347659 & 1.057642216 & 0.302826622 \\\text { Attendance } & 0.340583573 & 0.52852452 & 0.644404489 & 0.526635689 \\\hline\end{array}$$

-Referring to Table 13-6, which of the following statements is true?

A) If attendance increases by 1%, the estimated average score received will increase by 39.39 percentage points.
B) If the score received increases by 39.39%, the estimated average attendance will go up by 1%.
C) If attendance increases by 1%, the estimated average score received will increase by 0.341 percentage points.
D) If attendance increases by 0.341%, the estimated average score received will increase by 1 percentage point.

Question 55

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { ations } & 30 \\\hline\end{array}\end{array}$$

$\begin{array}{lrrccc}\hline & \text { d f } & \text { SS } & \text {MS} & \text { F } & \text { Significance F } \\\hline \text {Regression} & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text {Residual }& 28 & 3.1282 & 0.1117 & & \\ \text {Total }& 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text { Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value}& \text {Lower 95\%} & \text {Upper 95\%} \\\hline \text { Invoices }& 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text {Processed }& 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \\\hline\end{array}$






-Referring to Table 13-12, the error sum of squares (SSE) of the above regression is

A) 0.1117.
B) 29.0720.
C) 25.9438.
D) 3.1282.

Question 56

In performing a regression analysis involving two numerical variables, we are assuming

A) the variation around the line of regression is the same for each X value.
B) that X and Y are independent.
C) the variances of X and Y are equal.
D) all of the above

Question 57

TABLE 13- 11
A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:
$$\begin{array} { l c } & \text { Regression Statistics } \\\hline \text { Multiple R } & 0.8531 \\\text { R Square } & 0.7278 \\\text { Adjusted R Square } & 0.7180 \\\text { Standard Error } & 47.8668 \\\text { Observations } & 30\end{array}$$ ANOVA
$\begin{array}{lrrrrr}\hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\\hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\\text {Residual} & 28 & 64154.42 & 2291.23 & & \\\text {Total} & 29 & 235654.20 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\\hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\\hline\end{array}$




-Referring to Table 13-11, which of the following is the correct alternative hypothesis for testing whether there is a linear relationship between box office gross and home video unit sales?

A) $H_{1}: \beta_{1}=0$
B) $H_{1}: b_{1}=0$
C) $H_{1}: \beta_{1} \neq 0$
D) $H_{1}: b_{1} \neq 0$

Question 58

If the Durbin-Watson statistic has a value close to 4, which assumption is violated?

A) normality of the errors
B) homoscedasticity
C) independence of errors
D) none of the above

Question 59

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is the estimated slope parameter for the candy bar price and sales data?

A) 161.386
B) - 48.193
C) 0.784
D) - 3.810

Question 60

TABLE 13-8
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
$\text {Regressing GPA on \(\mathrm { ACT }\)}$
$$\begin{array}{l}\text { Regressing GPA on } \mathrm { ACT }\\\begin{array} { l c } \hline & \text { Regression Statistics } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard E rror } & 0.2691 \\\text { Observations } & 8\end{array}\end{array}$$

ANOVA
$\begin{array}{lcllcc}\hline & \text {d f} & \text {SS} & \text { MS }& \text { F } & \text { Significance F} \\\hline \text {Regression }&1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\ \text {Residual }& 6 & 0.4347 & 0.0724 & & \\ \text {Total }& 7 & 1.0287 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text {Standard Error }& \text {T Stat }& \text { p -value }& \text {Lower 95\%}& \text { Upper 95\% } \\\hline \text { Intercept} & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\ \text {ACT }& 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$



-Referring to Table 13-8, what is the predicted average value of GPA when ACT = 20?

A) 2.66
B) 2.61
C) 3.12
D) 2.80

Question 61

TABLE 13-8
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
$$\begin{array}{l}\text { Regressing GPA on } \mathrm { ACT }\\\begin{array} { l c } \hline & \text { Regression Statistics } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard E rror } & 0.2691 \\\text { Observations } & 8\end{array}\end{array}$$

ANOVA
$\begin{array}{lcllcc}\hline & \text {d f} & \text {SS} & \text { MS }& \text { F } & \text { Significance F} \\\hline \text {Regression }&1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\ \text {Residual }& 6 & 0.4347 & 0.0724 & & \\ \text {Total }& 7 & 1.0287 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text {Standard Error }& \text {T Stat }& \text { p -value }& \text {Lower 95\%}& \text { Upper 95\% } \\\hline \text { Intercept} & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\ \text {ACT }& 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$


-Referring to Table 13-8, what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

A) Do not reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.
B) Reject the null hypothesis; hence there is not sufficient evidence to show that ACT scores and GPA are linearly related.
C) Reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.
D) Do not reject the null hypothesis; hence there is not sufficient evidence to show that ACT scores and GPA are linearly related.

Question 62

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$$

-Referring to Table 13-2, to test that the regression coefficient, þ1, is not equal to 0, what would be the critical values? Use ? = 0.05.

A) ±3.1634
B) ±2.5706
C) ±2.7764
D) ±3.4954

Question 63

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$$

-Referring to Table 13-2, if the price of the candy bar is set at $2, the predicted sales will be

A) 90.
B) 65.
C) 100.
D) 30.

Question 64

The Y-intercept (b₀) represents the

A) change in estimated average Y per unit change in X.
B) predicted value of Y.
C) predicted value of Y when X = 0.
D) variation around the sample regression line.

Question 65

The residuals represent

A) the difference between the actual Y values and the predicted Y values.
B) the square root of the slope.
C) the predicted value of Y for the average X value.
D) the difference between the actual Y values and the mean of Y.

Question 66

TABLE 13-2
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { l l c } \hline \text { City } & \text { Price } ( \$ ) & \text { Sales } \\\hline \text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32 \\\hline\end{array}$$

-Referring to Table 13-2, what is the estimated average change in the sales of the candy bar if price goes up by $1.00?

A) - 3.810
B) - 48.193
C) 161.386
D) 0.784

Question 67

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { ations } & 30 \\\hline\end{array}\end{array}$$

$\begin{array}{lrrccc}\hline & \text { d f } & \text { SS } & \text {MS} & \text { F } & \text { Significance F } \\\hline \text {Regression} & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text {Residual }& 28 & 3.1282 & 0.1117 & & \\ \text {Total }& 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text { Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value}& \text {Lower 95\%} & \text {Upper 95\%} \\\hline \text { Invoices }& 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text {Processed }& 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \\\hline\end{array}$






-Referring to Table 13-12, the estimated average amount of time it takes to process one additional invoice is

A) 0.0126 more hours.
B) 0.0126 fewer hours.
C) 0.4024 more hours.
D) 0.4024 fewer hours.

Question 68

TABLE 13- 11
A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:
$$\begin{array} { l c } \hline & \text { Regression Stadistics } \\\hline \text { Multiple R } & 0.8531 \\\text { R Square } & 0.7278 \\\text { Adjusted R Square } & 0.7180 \\\text { Standard Error } & 47.8668 \\\text { Observations } & 30\end{array}$$ ANOVA
$\begin{array}{lrrrrr}\hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\\hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\\text {Residual} & 28 & 64154.42 & 2291.23 & & \\\text {Total} & 29 & 235654.20 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\\hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\\hline\end{array}$



-Referring to Table 13-11, what is the standard deviation around the regression line?

Question 69

TABLE 13-6
The following EXCEL tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.
$\begin{array}{ll}\hline \text {Regression Statistics } \\\hline \text { Multiple R} & 0.142620229 \\ \text {R Square} & 0.02034053 \\ \text {Adjusted R Square} & -0.028642444 \\ \text {Standard Error} & 20.25979924 \\ \text {Observations} & 22 \\\hline\end{array}$

$\begin{array}{lcrrc} & \text { Coefficients } & \text { Standard Enor } & {\text { T Stat }} & p \text {-value } \\\hline \text { Intercept } & 39.39027309 & 37.24347659 & 1.057642216 & 0.302826622 \\\text { Attendance } & 0.340583573 & 0.52852452 & 0.644404489 & 0.526635689 \\\hline\end{array}$


-Referring to Table 13-6, which of the following statements is true?

A) 2% of the total variability in percentage attendance can be explained by score received.
B) -2.86% of the total variability in percentage attendance can be explained by score received.
C) -2.86% of the total variability in score received can be explained by percentage attendance.
D) 2% of the total variability in score received can be explained by percentage attendance.

Question 70

TABLE 13-9
It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased.
Regression Stedistics
$\begin{array} { l l } \text { Multiple R } & 0.8857 \\ \text { RSquare } & 0.7845 \\ \text { Adjusted R Square } & 0.7801 \\ \text { Standard Error } & 1.3704 \end{array}$
Observations 51

ANOVA

$\begin{array}{lccrcc}\hline & d f & S S &{M S} & F & \text { Significance } F \\\hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 \\\text { Residual } & & & 1.8782 & \\\text { Total } & 50 & 427.0798 & &\end{array}$

$\begin{array}{lrccccr} & \text { Coeffcients } & \text { Standard Error } &t \text { Stat } & p-{\text {-value }} & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 2.051 \mathrm{E}-05 & -2.7015 & -1.0865 \\\text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm{E}-18 & 0.8321 & 1.1269 \\\hline\end{array}$


-Referring to Table 13-9, the p-value of the measured F-test statistic to test whether HOURS affects SALARY is

A) 2.051E-05.
B) (2.051E-05)/2.
C) 5.944E-18.
D) (5.944E-18)/2.

Question 71

TABLE 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { l l l } \hline \text { Student } & \text { CoopJobs } & \text { JobOffer } \\\hline 1 & 1 & 4 \\2 & 2 & 6 \\3 & 1 & 3 \\4 & 0 & 1\end{array}$$

-Referring to Table 13-3, the total sum of squares (SST) is _____.

Question 72

TABLE 13-01
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
$E(Y)=\beta_{0}+\beta_{1} X$
The results of the simple linear regression are provided below.
$\hat{Y}=-2,700+20 X, \mathrm{~S}_{Y X}=65, \text { two-tailed } p \text { value }=0.034\left(\text { for testing } \beta_{1}\right)$


-Referring to Table 13-1, interpret the estimate of þ0, the Y-intercept of the line.

A) About 95% of the observed service charges fall within $2,700 of the least squares line.
B) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700.
C) All companies will be charged at least $2,700 by the bank.
D) There is no practical interpretation since a sales revenue of $0 is a nonsensical value.

Question 73

TABLE 13- 11
A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8531 \\\text { RSquare } & 0.7278 \\\text { Adjusted R Square } & 0.7180 \\\text { Standard Error } & 47.8668 \\\text { Observations } & 30\end{array}\end{array}$$
ANOVA
$\begin{array}{lrrrrr}\hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\\hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\\text {Residual} & 28 & 64154.42 & 2291.23 & & \\\text {Total} & 29 & 235654.20 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\\hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\\hline\end{array}$



-Referring to Table 13-11, which of the following is the correct interpretation for the coefficient of determination?

A) 72.8% of the variation in the box office gross can be explained by the variation in the video unit sales.
B) 71.8% of the variation in the video unit sales can be explained by the variation in the box office gross.
C) 71.8% of the variation in the box office gross can be explained by the variation in the video unit sales.
D) 72.8% of the variation in the video unit sales can be explained by the variation in the box office gross.

Question 74

TABLE 13-8
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
Regressing GPA on $A C T$
$\begin{array}{lc}\text { Regression Statistics } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard Error } & 0.2691 \\\text { Observations } & 8\end{array}$
ANOVA
$\begin{array}{lccccc} & d f & S S & M S & F & \text { Significance } F \\\hline \text { Regression 1 } & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\\text { Residual } & 6 & 0.4347 & 0.0724 & & \\\text { Total } & 7 & 1.0287 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text {Standard Error }& \text {T Stat }& \text { p -value }& \text {Lower 95\%}& \text { Upper 95\% } \\\hline \text { Intercept} & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\ \text {ACT }& 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}$



-Referring to Table 13-8, the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT is

A) 0.7598.
B) 0.0356.
C) 0.1021.
D) 2.8633.

Question 75

TABLE 13-10
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | l | l | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Table 13-10, what is the value of the coefficient of correlation?

Question 76

TABLE 13-12
The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.9947 \\\text { R Square } & 0.8924 \\\text { Adjusted R Square } & 0.8886 \\\text { Standard Error } & 0.3342 \\\text { ations } & 30 \\\hline\end{array}\end{array}$$

$\begin{array}{lrrccc}\hline & \text { d f } & \text { SS } & \text {MS} & \text { F } & \text { Significance F } \\\hline \text {Regression} & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\ \text {Residual }& 28 & 3.1282 & 0.1117 & & \\ \text {Total }& 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrr}\hline & \text { Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value}& \text {Lower 95\%} & \text {Upper 95\%} \\\hline \text { Invoices }& 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\ \text {Processed }& 0.0126 & 0.0008 & 15.2388 & 4.3946 \mathrm{E}-15 & 0.0109 & 0.0143 \\\hline\end{array}$






-Referring to Table 13-12, the value of the measured t-test statistic to test whether the amount of time depends linearly on the number of invoices processed is

A) 0.8924.
B) 15.2388.
C) 232.2200.
D) 3.2559.

Question 77

TABLE 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { l l l } \hline \text { Student } & \text { CoopJobs } & \text { JobOffer } \\\hline 1 & 1 & 4 \\2 & 2 & 6 \\3 & 1 & 3 \\4 & 0 & 1\end{array}$$

-Referring to Table 13-3, suppose the director of cooperative education wants to obtain a 95% confidence-interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The t critical value she would use is_______

Question 78

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

A) homoscedasticity
B) normality of the errors
C) independence of errors
D) none of the above

Question 79

TABLE 13-7
An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following EXCEL output.
$$\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Error } & \text { T Stat } & { p \text {-value } } \\\hline \text { Intercept } & 4.866004258 & 0.35743609 & 13.61363441 & 8.7932 \mathrm { E } - 13 \\\text { S\& P } & - 0.502513506 & 0.071597152 &- 7.01862425 & 294942 \mathrm { E } - 07 \\\hline\end{array}$$

-Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the appropriate null and alternative hypotheses are, respectively,

A) $H_{0}: r \leq 0$ versus $H_{1}: r>0$ .
B) $H_{0}: r \geq 0$ versus $H_{1}: r<0$ .
C) $H_{0}: \rho \geq 0$ versus $H_{1}: \rho<0$ .
D) $H_{0}: \rho \leq 0$ versus $H_{1}: \rho>0$ .

Question 80

TABLE 13-5
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data with the following results:
$\begin{array}{ll}\text { Regression Sttuistics } \\\hline \text { Multiple R } & 0.802 \\\text { R Square } & 0.643 \\\text { Adjusted RSquare } & 0.618 \\\text { Standard Error SYX } & 0.9224\end{array}$

Observations 16
ANOVA

$\begin{array}{lrlrlr} & d f & \text { SS } & \text { MS } & F & \text { Sig.F } \\\hline \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\\text { Error } & 14 & 11.912 & 0.851 & & \\\text { Total } & 15 & 33.409 & & &\end{array}$

$\begin{array}{l}\begin{array}{lllrl}\hline \text { Predictor}& \text { Coeffcients } & \text { Standard Error } & \text { tStat } & \text { p-value } \\\text { Intercept } & 3.962 & 1.440 & 2.75 & 0.016 \\\text { Industry } & 0.040451 & 0.008048 & 5.03 & 0.000 \\\hline\end{array}\\\text { Durbin- Watson Statistic } 1.59\end{array}$


-Referring to Table 13-5, the standard error of the estimated slope coefficient is________ .