Question 1

If two variables, x and y, have a strong linear relationship, then

Accepted Answer

A)  there may or may not be any causal relationship between x and y 
B)  x causes y to happen 
C)  y causes x to happen 
D)  None of these alternatives is correct. 
A)  there may or may not be any causal relationship between x and y 
B)  x causes y to happen 
C)  y causes x to happen 
D)  None of these alternatives is correct.

Question 2

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
 $\hat { Y }$ n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. The t statistic for testing the significance of the slope is

Accepted Answer

A)  1.80 
B)  1.96 
C)  6.708 
D)  0.555 
A)  1.80 
B)  1.96 
C)  6.708 
D)  0.555

Question 3

Exhibit 12-9
A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x).
 $\begin{array}{ll}
\Sigma \mathrm{X}=90 & \Sigma \mathrm{Y}-{\bar{\mathrm{Y}}) X}-\bar{X})=466 \
\Sigma \mathrm{Y}=170 & \Sigma \mathrm{Y}-\overline{\mathrm{Y}})^{2}=1434 \
\mathrm{n}=10\
\mathrm{SSE}=505.98 &  \Sigma \mathrm{X}-\bar{X})^{2}=234 
\end{array}$

-Refer to Exhibit 12-9. The coefficient of determination equals

Accepted Answer

A)  0.6472 
B)  -0.6472 
C)  0 
D)  1 
A)  0.6472 
B)  -0.6472 
C)  0 
D)  1

Question 4

In regression analysis, the independent variable is

Accepted Answer

A)  used to predict other independent variables 
B)  used to predict the dependent variable 
C)  called the intervening variable 
D)  the variable that is being predicted 
A)  used to predict other independent variables 
B)  used to predict the dependent variable 
C)  called the intervening variable 
D)  the variable that is being predicted

Question 5

Below you are given a partial computer output based on a sample of 21 observations, relating an independent variable x) and a dependent variable y).
 $$\begin{array} { l c c } 
\text { Predictor } & \text { Coefificient } & \text { Standard Error } \
\text { Canstant } & 30.139&1.181 \
\text { X } & -0.252&0.022
\end{array}$$ Analysis of Variance
SOURCE SS
Regression 1,759.481
Error 259.186 
a. Develop the estimated regression line.
b. At α = 0.05, test for the significance of the slope.
c. At α = 0.05, perform an F test.
d. Determine the coefficient of determination.
e. Determine the coefficient of correlation.

Accepted Answer

a. @#IMG-DLM& = 30.139 - 0.252X
b. t = -

Question 6

Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below.
 $\begin{array}{cc}\text { Hours of Television }&\text { Age }\
1 & 45 \
3 & 30 \
4 & 22 \
3 & 25 \
6 & 5
\end{array}$ 
a. Determine which variable is the dependent variable.
b. Compute the least squares estimated line.
c. Is there a significant relationship between the two variables? Use a .05 level of significance. Be sure to state the null and alternative hypotheses.
d. Compute the coefficient of determination. How would you interpret this value?

Accepted Answer

a. Hours of Television 
b. @#IMG-DLM& = 6.564 - 0.

Question 7

Correlation analysis is used to determine

Accepted Answer

A)  the equation of the regression line 
B)  the strength of the relationship between the dependent and the independent variables 
C)  a specific value of the dependent variable for a given value of the independent variable 
D)  None of these alternatives is correct. 
A)  the equation of the regression line 
B)  the strength of the relationship between the dependent and the independent variables 
C)  a specific value of the dependent variable for a given value of the independent variable 
D)  None of these alternatives is correct.

Question 8

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

Accepted Answer

A)  0.80% 
B)  80% 
C)  0.64% 
D)  64% 
A)  0.80% 
B)  80% 
C)  0.64% 
D)  64%

Question 9

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is

Accepted Answer

A)  0.65 
B)  0.1785 
C)  any positive value 
D)  any value 
A)  0.65 
B)  0.1785 
C)  any positive value 
D)  any value

Question 10

Below you are given information on annual income and years of college education.
 $\begin{array}{cc}\text { Income In Thousands) }&\text { Years of College }\
28 & 0 \
40 & 3 \
36 & 2 \
28 & 1 \
48 & 4
\end{array}$ 
a. Develop the least squares regression equation.
b. Estimate the yearly income of an individual with 6 years of college education.
c. Compute the coefficient of determination.
d. Use a t test to determine whether the slope is significantly different from zero. Let α = 0.05.
e. At 95% confidence, perform an F test and determine whether or not the model is significant.

Accepted Answer

a. @#IMG-DLM& = 25.6 + 5.2X
b. $56,800
c. 0.939
d.

Question 11

Below you are given information on a woman's age and her annual expenditure on purchase of books.
 $\begin{array}{ll}\text { Age }&\text { Annual Expenditure \$) }\
18 & 210 \
22 & 180 \
21 & 220 \
28 & 280
\end{array}$ 
a. Develop the least squares regression equation.
b. Compute the coefficient of determination.
c. Use a t test to determine whether the slope is significantly different from zero. Let α = 0.05.
d. At 95% confidence, perform an F test and determine whether or not the model is significant.

Accepted Answer

a. @#IMG-DLM& = 54.834 + 7.536X 
b. R² = 0.568
c.

Question 12

Compared to the confidence interval estimate for a particular value of y in a linear regression model), the interval estimate for an average value of y will be

Accepted Answer

A)  narrower 
B)  wider 
C)  the same 
D)  None of these alternatives is correct. 
A)  narrower 
B)  wider 
C)  the same 
D)  None of these alternatives is correct.

Question 13

If the coefficient of determination is a positive value, then the coefficient of correlation

Accepted Answer

A)  must also be positive 
B)  must be zero 
C)  can be either negative or positive 
D)  must be larger than 1 
A)  must also be positive 
B)  must be zero 
C)  can be either negative or positive 
D)  must be larger than 1

Question 14

Exhibit 12-9
A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x).
 $\begin{array}{ll}
\Sigma \mathrm{X}=90 & \Sigma \mathrm{Y}-{\bar{\mathrm{Y}}) X}-\bar{X})=466 \
\Sigma \mathrm{Y}=170 & \Sigma \mathrm{Y}-\overline{\mathrm{Y}})^{2}=1434 \
\mathrm{n}=10\
\mathrm{SSE}=505.98 &  \Sigma \mathrm{X}-\bar{X})^{2}=234 
\end{array}$

-Refer to Exhibit 12-9. The least squares estimate of b? equals

Accepted Answer

A)  0.923 
B)  1.991 
C)  -1.991 
D)  -0.923 
A)  0.923 
B)  1.991 
C)  -1.991 
D)  -0.923

Question 15

The owner of a retail store randomly selected the following weekly data on profits and advertising cost.
 $\begin{array}{ccc}\text { Week }&\text { Advertising Cost \$) }&\text { Profit } \$\
1 & 0 & 200 \
2 & 50 & 270 \
3 & 250 & 420 \
4 & 150 & 300 \
5 & 125 & 325
\end{array}$ 
a. Write down the appropriate linear relationship between advertising cost and profits. Which is the dependent variable? Which is the independent variable?
b. Calculate the least squares estimated regression line.
c. Predict the profits for a week when $200 is spent on advertising.
d. At 95% confidence, test to determine if the relationship between advertising costs and profits is statistically significant.
e. Calculate the coefficient of determination.

Accepted Answer

a. EY) = β₀ + β₁X, where Y is profit and

Question 16

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
 $\hat { Y }$ n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. The F statistic computed from the above data is

Accepted Answer

A)  3 
B)  45 
C)  48 
D)  50 
A)  3 
B)  45 
C)  48 
D)  50

Question 17

Exhibit 12-8
The following information regarding a dependent variable Y and an independent variable X is provided
 $$\begin{array} { l } 
\mathrm { n } = 4 \
\Sigma \mathrm { X } = 90 \
\Sigma \mathrm { Y } = 340 \
\Sigma \mathrm { Y } -  { \bar { Y) } \mathrm { X } } - \bar { X } ) = - 156 \
\Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 234 \
\Sigma \mathrm { Y } - \bar { Y } ) ^ { 2 } = 1974 \
\mathrm { SSR } = 104
\end{array}$$
-Refer to Exhibit 12-8. The coefficient of correlation is

Accepted Answer

A)  -0.2295 
B)  0.2295 
C)  0.0527 
D)  -0.0572 
A)  -0.2295 
B)  0.2295 
C)  0.0527 
D)  -0.0572

Question 18

In regression analysis, which of the following is not a required assumption about the error term ε?

Accepted Answer

A)  The expected value of the error term is one. 
B)  The variance of the error term is the same for all values of X. 
C)  The values of the error term are independent. 
D)  The error term is normally distributed. 
A)  The expected value of the error term is one. 
B)  The variance of the error term is the same for all values of X. 
C)  The values of the error term are independent. 
D)  The error term is normally distributed.

Question 19

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 months was taken. The results of the sample are presented below. The estimated least squares regression equation is
= 75.061 - 6.254X
 $\hat { Y }$ Y X
Monthly Sales Interest Rate In Percent)
22 9.2
20 7.6
10 10.4
45 5.3 
a. Obtain a measure of how well the estimated regression line fits the data.
b. You want to test to see if there is a significant relationship between the interest rate and monthly sales at the 1% level of significance. State the null and alternative hypotheses.
c. At 99% confidence, test the hypotheses.
d. Construct a 99% confidence interval for the average monthly sales for all months with a 10% interest rate.
e. Construct a 99% confidence interval for the monthly sales of one month with a 10% interest rate.

Accepted Answer

a. R² = 0.8687
b. H0: β₁ = 0
Ha: β₁ ≠ 0

Question 20

Exhibit 12-7
You are given the following information about y and x.
 $$\begin{array} { c c } 
\text { Dependent Varinble } Y )& \text { Independent Varinble X)} \ \end{array}$$  5 4
7 6
9 2
11 4
-Refer to Exhibit 12-7. The coefficient of determination equals

Accepted Answer

A)  0.3162 
B)  -0.3162 
C)  0.10 
D)  -0.10 
A)  0.3162 
B)  -0.3162 
C)  0.10 
D)  -0.10

If two variables, x and y, have a strong linear relationship, then

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x). \Sigma=90 \Sigma- )X -)=466 \Sigma=170 \Sigma-=1434 =10 =505.98 \Sigma-=234 -Refer to Exhibit 12-9. The coefficient of determination equals

In regression analysis, the independent variable is

Correlation analysis is used to determine

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is

Compared to the confidence interval estimate for a particular value of y in a linear regression model), the interval estimate for an average value of y will be

If the coefficient of determination is a positive value, then the coefficient of correlation

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x). \Sigma=90 \Sigma- )X -)=466 \Sigma=170 \Sigma-=1434 =10 =505.98 \Sigma-=234 -Refer to Exhibit 12-9. The least squares estimate of b? equals

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x $\hat { Y }$ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. The F statistic computed from the above data is

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided =4 \Sigma=90 \Sigma=340 \Sigma- -)=-156 \Sigma-=234 \Sigma-=1974 =104 -Refer to Exhibit 12-8. The coefficient of correlation is

In regression analysis, which of the following is not a required assumption about the error term ε?

Exhibit 12-7 You are given the following information about y and x. Dependent Varinble Y) Independent Varinble X) 5 4 7 6 9 2 11 4 -Refer to Exhibit 12-7. The coefficient of determination equals

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Exam 12: Simple Linear Regression

If two variables, x and y, have a strong linear relationship, then

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x). \Sigma=90 \Sigma- )X -)=466 \Sigma=170 \Sigma-=1434 =10 =505.98 \Sigma-=234 -Refer to Exhibit 12-9. The coefficient of determination equals

In regression analysis, the independent variable is

Correlation analysis is used to determine

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is

Compared to the confidence interval estimate for a particular value of y in a linear regression model), the interval estimate for an average value of y will be

If the coefficient of determination is a positive value, then the coefficient of correlation

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x). \Sigma=90 \Sigma- )X -)=466 \Sigma=170 \Sigma-=1434 =10 =505.98 \Sigma-=234 -Refer to Exhibit 12-9. The least squares estimate of b? equals

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x Y^\hat { Y }Y^ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. The F statistic computed from the above data is

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided =4 \Sigma=90 \Sigma=340 \Sigma- -)=-156 \Sigma-=234 \Sigma-=1974 =104 -Refer to Exhibit 12-8. The coefficient of correlation is

In regression analysis, which of the following is not a required assumption about the error term ε?

Exhibit 12-7 You are given the following information about y and x. Dependent Varinble Y) Independent Varinble X) 5 4 7 6 9 2 11 4 -Refer to Exhibit 12-7. The coefficient of determination equals

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Multiple Regression

Filters

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x $\hat { Y }$ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. The F statistic computed from the above data is