Deck 13: Simple Linear Regression

Question 1

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

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

Answer 1

C

Question 2

SCENARIO 13-2
Referring to Scenario 13-2, what is the estimated mean change in the sales of the candy bar if
Price goes up by $1.00?

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

Answer 2

D

Question 3

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

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

Answer 3

D

Question 4

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

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

Question 5

Question 6

SCENARIO 13-1
Referring to Scenario 13-1, interpret the estimate of , the Y-intercept of the line.

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

Question 7

SCENARIO 13-2

Question 8

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

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

Question 9

SCENARIO 13-2

Question 10

SCENARIO 13-2
Referring to Scenario 13-2, what is the standard error of the regression slope estimate, Sb1 ?

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

Question 11

Question 12

Question 13

SCENARIO 13-1
Referring to Scenario 13-1, interpret the estimate of , 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 $65 of the least squares line.
B) About 95% of the observed service charges equal their corresponding predicted values.
C) About 95% of the observed service charges fall within $130 of the least squares line.
D) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

Question 14

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

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

Question 15

SCENARIO 13-2
Referring to Scenario 13-2, if the price of the candy bar is set at $2, the estimated mean sales will
Be

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

Question 16

SCENARIO 13-2

Question 17

The Y-intercept (b0)represents the

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

Question 18

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

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

Question 19

The least squares method minimizes which of the following?

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

Question 20

The Y-intercept (b0)represents the

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

Question 21

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0.For a test with a level of significance of 0.01, the null
hypothesis should be rejected if the value of the test statistic is ________.

Question 22

SCENARIO 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.
Referring to Scenario 13-6, which of the following statements is true?

A) 14.26% of the total variability in score received can be explained by percentage attendance.
B) 14.2% of the total variability in percentage attendance can be explained by score received.
C) 2% of the total variability in score received can be explained by percentage attendance.
D) 2% of the total variability in percentage attendance can be explained by score received.

Question 23

The residual represents the discrepancy between the observed dependent variable and its
_______ value.

Question 24

SCENARIO 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 3.0.The value of the test statistic is ________.

Question 25

True of False: The Chancellor of a university has commissioned a team to collect data on
students' GPAs and the amount of time they spend bar hopping every week (measured in
minutes).He wants to know if imposing much tougher regulations on all campus bars to make it
more difficult for students to spend time in any campus bar will have a significant impact on
general students' GPAs.His team should use a t test on the slope of the population regression.

Question 26

SCENARIO 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 0.For a test with a level of significance of 0.05, the null
hypothesis should be rejected if the value of the test statistic is ________.

Question 27

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated.The
p-value of the test is ________.

Question 28

SCENARIO 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 to analyze the last 4 years of quarterly data with
the following results: Durbin-Watson Statistic 1.59
Referring to Scenario 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 evidence of autocorrelation.
B) the test is unable to make a definite conclusion.
C) there is no evidence of autocorrelation.
D) there is not enough information to perform the test.

Question 29

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0.At a level of significance of 0.01, the decision that should be
made implies that _____ (there is a or there is no)linear dependent relationship between the
independent and dependent variables.

Question 30

SCENARIO 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 to analyze the last 4 years of quarterly data with
the following results: Durbin-Watson Statistic 1.59
If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

A) Normality of the errors.
B) Independence of errors.
C) Homoscedasticity.
D) None of the above.

Question 31

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated.At a
level of significance of 0.01, the decision that should be made implies that the number of new
clients brought in _____ (had or did not have)a positive impact on the amount of sales
generated.

Question 32

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated.For
a test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the
test statistic is ________.

Question 33

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0.At a level of significance of 0.01, the null hypothesis should
be _______ (rejected or not rejected).

Question 34

SCENARIO 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 to analyze the last 4 years of quarterly data with
the following results: Durbin-Watson Statistic 1.59
If the Durbin-Watson statistic has a value close to 4, which assumption is violated?

A) Normality of the errors.
B) Independence of errors.
C) Homoscedasticity.
D) None of the above.

Question 35

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated.At a
level of significance of 0.01, the null hypothesis should be _______ (rejected or not rejected).

Question 36

SCENARIO 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 to analyze the last 4 years of quarterly data with
the following results: Durbin-Watson Statistic 1.59
The standard error of the estimate is a measure of

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

Question 37

SCENARIO 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 to analyze the last 4 years of quarterly data with
the following results: Durbin-Watson Statistic 1.59

Question 38

SCENARIO 13-4
Simple Linear Regression 13-13
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0.The p-value of the test is ________.

Question 39

SCENARIO 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 3.0.For a test with a level of significance of 0.05, the null
hypothesis should be rejected if the value of the test statistic is ________.

Question 40

SCENARIO 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.
Referring to Scenario 13-3, set up a scatter plot.

Question 41

True or False: The Regression Sum of Squares (SSR)can never be greater than the Total Sum of
Squares (SST).

Question 42

In a simple linear regression problem, r and b1

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

Question 43

Question 44

Question 45

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

A) Normality.
B) Homoscedasticity.
C) Independence of errors.
D) No assumptions are violated, the graph should resemble a fan.

Question 46

The residuals represent

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

Question 47

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

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

Question 48

True or False: Data that exhibit an autocorrelation effect violate the regression assumption of
independence.

Question 49

True or False: The value of r is always positive.

Question 50

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 straight line with a positive slope.
D) all the data points must fall exactly on a horizontal straight line with a zero slope.

Question 51

True or False: Regression analysis is used for prediction, while correlation analysis is used to
measure the strength of the association between two numerical variables.

Question 52

If the residuals in a regression analysis of time-ordered data are not correlated, the value of the
Durbin-Watson D statistic should be near __________.

Question 53

Assuming a linear relationship between X and Y, if the coefficient of correlation (r)equals
- 0)30,

Question 54

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

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

Question 55

True or False: The coefficient of determination represents the ratio of SSR to SST.

Question 56

SCENARIO 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.
Referring to Scenario 13-6, which of the following statements is true?

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

Question 57

Question 58

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

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

Question 59

True or False: The Durbin-Watson D statistic is used to check the assumption of normality.

Question 60

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

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

Question 61

SCENARIO 13-7
Referring to Scenario 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) -7.019
B) -0.503
C) 0.072
D) 0.357

Question 62

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

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

Question 63

Question 64

Question 65

SCENARIO 13-11
A computer software developer would like to use the number of downloads (in thousands)for the trial
version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make
on the full version of the new shareware.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
sharewares that he has developed:
Simple Linear Regression 13-43
Referring to Scenario 13-11, predict the revenue when the number of downloads is 30
thousands.

Question 66

SCENARIO 13-9
Referring to Scenario 13-9, the estimated change in mean salary (in thousands of dollars)as a
Result of spending an extra hour per day studying is

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

Question 67

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

Question 68

SCENARIO 13-11
A computer software developer would like to use the number of downloads (in thousands)for the trial
version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make
on the full version of the new shareware.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
sharewares that he has developed:
Simple Linear Regression 13-43
Referring to Scenario 13-11, which of the following is the correct interpretation for the slope
Coefficient?

A) For each decrease of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands.
B) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands.
C) For each decrease of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.
D) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.

Question 69

SCENARIO 13-8

Question 70

SCENARIO 13-9
Referring to Scenario 13-9, the value of the measured t-test statistic to test whether mean
SALARY depends linearly on HOURS is

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

Question 71

SCENARIO 13-8
Referring to Scenario 13-8, the interpretation of the coefficient of determination in this
Regression is

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

Question 72

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

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

Question 73

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

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

Question 74

SCENARIO 13-11
A computer software developer would like to use the number of downloads (in thousands)for the trial
version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make
on the full version of the new shareware.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
sharewares that he has developed:
Simple Linear Regression 13-43
Referring to Scenario 13-11, which of the following is the correct interpretation for the
Coefficient of determination?

A) 74.67% of the variation in revenue can be explained by the variation in the number of downloads.
B) 75.54% of the variation in revenue can be explained by the variation in the number of downloads.
C) 74.67% of the variation in the number of downloads can be explained by the variation in revenue.
D) 75.54% of the variation in the number of downloads can be explained by the variation in revenue.

Question 75

SCENARIO 13-8
Referring to Scenario 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 insufficient evidence to show that ACT scores and GPA are linearly related.
B) Reject the null hypothesis; hence there is insufficient evidence to show that ACT scores and GPA are linearly related.
C) Do not reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.
D) Reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.

Question 76

True or False: When r = - 1, it indicates a perfect relationship between X and Y.

Question 77

SCENARIO 13-11
A computer software developer would like to use the number of downloads (in thousands)for the trial
version of his new shareware to predict the amount of revenue (in thousands of dollars)he can make
on the full version of the new shareware.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
sharewares that he has developed:
Simple Linear Regression 13-43
Referring to Scenario 13-11, what is the standard error of estimate?

Question 78

SCENARIO 13-7
Referring to Scenario 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,

Question 79

Question 80