Deck 11: Multiple Regression

Question 1

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. The researcher also ran the simple linear regression model
Deaths = ₀ + ₂(Income)+ _i.
The following results were obtained from statistical software: What is the value of R² in the simple linear regression model?

A)0.014
B)0.020
C)0.688
D)0.941

Answer 1

0.014

Question 2

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose we wish to test the hypotheses H₀: ₁ = ₂ = 0 versus H_a: at least one of the _j is not 0 using the ANOVA F test.What can we say about the P-value for the ANOVA F test?

A)P-value < 0.001
B)0.001 C)0.005 D)P-value > 0.01

Answer 2

P-value < 0.001

Question 3

Based on a sample of the salaries of professors at a major university,you have performed a multiple linear regression relating salary to years of service and gender.The data included information on the following variables. The estimated multiple linear regression model is Salary = 45 + 3(Years)+ 4(Gender)+ 1(Years)(Gender).
Using the multiple linear regression equation,what would you estimate the average difference in the salaries of a male professor with 3 years of service and a female professor with 3 years of service to be?

A)$3000
B)$4000
C)$5000
D)$7000

Answer 3

$7000

Question 4

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. The researcher also ran the simple linear regression model
Deaths = ₀ + ₂(Income)+ _i.
The following results were obtained from statistical software: Based on the above results,the researcher tested the hypotheses H₀: ₂ = 0 versus H_a: ₂  0.What do we know about the P-value of the test?

A)P-value < 0.025
B)0.025
C)0.05
D)P-value > 0.10

Question 5

In a multiple regression with three explanatory variables,the total sum of squares SST = 1008,the model mean square MSM = 76,and the test statistic F = 2.533.How many observations were used?

A)26
B)29
C)30
D)31

Question 6

In a multiple regression with two explanatory variables,the total sum of squares SST = 1000 and the mean square error MSE = 40.There are 13 observations.What is the value of R²?

A)0.04
B)0.52
C)0.60
D)0.96

Question 7

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. What is a 95% confidence interval for the coefficient of promotional expenditures?

A)(-0.441,4.055)
B)(-0.312,3.926)
C)(-0.053,3.667)
D)(0.726,2.888)

Question 8

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. What is the estimate for the error variance  ²?

A)9.604
B)12.960
C)92.245
D)1937.137

Question 9

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. In an attempt to increase sales,the company can only directly influence some of these variables.It cannot change the number of competitors;it cannot change the district potential.The only two variables they can actively change are the number of active accounts and the promotional expenditures.Suppose they have $5000 to spend on new commercials (that is,promotional expenditures).By how much are sales expected to increase?

A)1.807 squares
B)9.035 squares
C)1807 squares
D)9035 squares

Question 10

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. The researcher also ran the simple linear regression model
Deaths = ₀ + ₂(Income)+ _i.
The following results were obtained from statistical software: Based on the analyses,what can we conclude?

A)The variable income is statistically significant at level 0.05 as a predictor of the variable deaths.
B)The variable income is statistically significant at level 0.05 as a predictor of the variable deaths in a multiple regression model that includes the variable children.
C)The variable income is not useful as a predictor of the variable deaths and should be omitted from the analysis.
D)The variable children is not useful as a predictor of the variable deaths,unless the variable income is also present in the multiple regression model.

Question 11

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. The researcher also ran the simple linear regression model
Deaths = ₀ + ₂(Income)+ _i.
The following results were obtained from statistical software: What can we conclude regarding the meaningfulness of the analyses?

A)They are very meaningful because the results are based on a very large sample consisting of the people in all 50 states as well as Washington,DC.
B)They are meaningful because R² for the multiple regression model is quite large,suggesting that the model fits well and the assumptions about the model are reasonable.
C)They are moderately meaningful because the results are based on a fairly large sample and they are at least consistent with what one would expect.They would be very meaningful if,in addition,we had examined the residuals and found no outliers or influential observations.
D)They are not necessarily meaningful because these results are based on available data.

Question 12

In a multiple regression with four explanatory variables,data are collected on 25 observations.What is the largest value the ANOVA F statistic can take on before we would reject the null hypothesis that all of the regression coefficients are zero,at the 5% significance level?

A)2.78
B)2.87
C)3.10
D)3.51

Question 13

What proportion of the variation in the variable deaths is explained by the explanatory variables children and income?

A)0.059
B)0.159
C)0.470
D)0.941

Question 14

In a multiple regression with five explanatory variables,data are collected on 63 observations.What are the degrees of freedom for the ANOVA F test?

A)4 and 57
B)5 and 57
C)5 and 58
D)5 and 62

Question 15

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose we wish to test the hypotheses H₀: ₁ = ₂ = 0 versus H_a: at least one of the _j is not 0 using the ANOVA F test.What is the value of the F statistic?

A)0.94
B)15.9
C)24
D)381.5

Question 16

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. What proportion of the variation in sales is explained by the set of all four explanatory variables?

A)-0.647
B)0.558
C)0.989
D)0.995

Question 17

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. Which of the four explanatory variables seems to be the least significant in the model?

A)Expenditures
B)Accounts
C)Competing brands
D)District potential

Question 18

A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = ₀ + ₁(Children)+ ₂(Income)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. What is a 99% confidence interval for ₂,the coefficient of the variable income?

A)-0.039 ± 0.030
B)-0.039 ± 0.040
C)0.015 ± 0.079
D)0.015 ± 0.104

Question 19

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. An F test for the two coefficients of promotional expenditures and district potential is performed.The hypotheses are H₀: ₁ = ₄ = 0 versus H_a: at least one of the _j is not 0.The F statistic for this test is 1.482 with 2 and 21 degrees of freedom.What can we say about the P-value for this test?

A)P-value < 0.025
B)0.025
C)0.05
D)P-value > 0.10

Question 20

The data referred to in this question were collected from several sales districts across the country.The data represent sales for a maker of asphalt roofing shingles.Information on the following variables is available. Partial SPSS regression output of a multiple regression model with sales as the response variable and the other four variables as predictor variables are given below. How many districts were sampled in all?

A)21
B)24
C)25
D)26

Question 21

Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. A graph of the residuals versus the predicted values is given below. What assumption do we check with this graph?

A)The Normality of the error terms
B)The independence of the residuals
C)The constant variance assumption of the predicted values
D)None of the above

Question 22

A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = ₀ + ₁($ per pupil)+ ₂(% taking)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose we wish to test the hypotheses H₀: ₁ = ₂ = 0 versus H_a: at least one of the _j is not 0,using the ANOVA F test.What is the value of the F statistic?

A)3.32
B)24.0
C)79.65
D)159.3

Question 23

Researchers at a car resale company are trying to build a model to predict a car's 4-year resale value (in thousands of dollars)from several predictor variables.The variables they selected are as below. Data were collected on cars of different models made by different manufacturers.SPSS output for the least-squares regression model is given below. A Normal quantile plot of the residuals is given below. What assumption do we check with this graph,and does the assumption seem to be satisfied?

Question 24

Based on a sample of the salaries of professors at a major university,you have performed a multiple linear regression relating salary to years of service and gender.The data included information on the following variables. The estimated multiple linear regression model is Salary = 45 + 3(Years)+ 4(Gender)+ 1(Years)(Gender).
A particular female professor with 6 years of experience currently has a salary of $60,000.What is the residual for this observation?

A)-$9000
B)-$3000
C)$3000
D)$9000

Question 25

A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = ₀ + ₁($ per pupil)+ ₂(% taking)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. What proportion of the variation in the variable SATM is explained by the explanatory variables $ per pupil and % taking?

A)0.232
B)0.301
C)0.768
D)0.960

Question 26

A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = ₀ + ₁($ per pupil)+ ₂(% taking)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Another researcher,using the same data,ran the simple linear regression model
SATM = ₀ + ₁($ per pupil)+ _i.
The following results were obtained from statistical software. The first researcher concluded that because the coefficient for the variable $ per pupil was positive in her results,spending additional money on students would have a positive effect on SATM scores.This researcher therefore recommended more money be spent on students.The second researcher concluded that because the coefficient for the variable $ per pupil was negative in his results,spending additional money on students would have a negative effect on SATM scores.This researcher therefore recommended less money be spent on students.Why are these two conclusions different even though the researchers used the same data?

A)An error must have been made by one of the researchers.
B)Both researchers failed to take into account that in their analyses,₁,the coefficient of the variable $ per pupil,was not statistically significant at even the 0.10 significance level.Hence,neither researcher could conclude that ₁ was significantly different from zero.
C)The researchers did not use the same set of explanatory variables in their models.
D)There must have been an influential observation in the data,rendering the analyses inappropriate.

Question 27

Researchers at a car resale company are trying to build a model to predict a car's 4-year resale value (in thousands of dollars)from several predictor variables.The variables they selected are as below. Data were collected on cars of different models made by different manufacturers.SPSS output for the least-squares regression model is given below. A particular car (not a truck)cost $40,000 and has an engine of 3.8 liters.What do you predict the 4-year resale value of this car to be?

Question 28

Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. What percentage of the variation in percent body fat remains unexplained,even after introducing weight and abdomen circumference into the model?

A)7.86%
B)15.11%
C)84.89%
D)92.14%

Question 29

Researchers at a car resale company are trying to build a model to predict a car's 4-year resale value (in thousands of dollars)from several predictor variables.The variables they selected are as below. Data were collected on cars of different models made by different manufacturers.SPSS output for the least-squares regression model is given below. Suppose we wish to test the hypotheses H₀: ₁ = 0 versus H_a: ₁  0,where ₁ is the coefficient for the variable type.Based on the 95% confidence interval given in the output,what do we know about the value of the P-value of this test?

Question 30

Based on a sample of the salaries of professors at a major university,you have performed a multiple linear regression relating salary to years of service and gender.The data included information on the following variables. The estimated multiple linear regression model is Salary = 45 + 3(Years)+ 4(Gender)+ 1(Years)(Gender).
Using the multiple linear regression equation,what would you estimate the average salary of male professors with 3 years of experience to be?

A)$53,000
B)$54,000
C)$58,000
D)$61,000

Question 31

A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = ₀ + ₁($ per pupil)+ ₂(% taking)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. What is the value of the MSE?

A)10.30
B)288.23
C)13835.10
D)22957.50

Question 32

Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. How many people were included in the study?

A)46
B)48
C)49
D)50

Question 33

A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = ₀ + ₁($ per pupil)+ ₂(% taking)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. What is an approximate 95% confidence interval for ₁,the coefficient of the variable $ per pupil?

A)0.00639 ± 0.0025
B)0.00639 ± 0.0042
C)0.00639 ± 0.0050
D)0.00639 ± 0.0067

Question 34

A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = ₀ + ₁($ per pupil)+ ₂(% taking)+ _i,
Where the deviations _i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of .This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Another researcher,using the same data,ran the simple linear regression model
SATM = ₀ + ₁($ per pupil)+ _i.
The following results were obtained from statistical software. Based on these results,a 95% confidence interval for ₁,the coefficient of the variable $ per pupil,is approximately

A)-0.012169 ± 0.0031.
B)-0.012169 ± 0.0052.
C)-0.012169 ± 0.0062.
D)-0.012169 ± 0.0083.

Question 35

Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. What is a 90% confidence interval for ₁,the coefficient of weight,based on these results?

A)-0.162 ± 0.038
B)-0.162 ± 0.064
C)-0.162 ± 0.525
D)-0.162 ± 4.230

Question 36

Researchers at a car resale company are trying to build a model to predict a car's 4-year resale value (in thousands of dollars)from several predictor variables.The variables they selected are as below. Data were collected on cars of different models made by different manufacturers.SPSS output for the least-squares regression model is given below. An F test for the two coefficients of type and engine is performed.The hypotheses areH₀: ₁ = ₃ = 0 versus H_a: at least one of the _j is not 0.The F statistic for this test is 12.21 with 2 and 115 degrees of freedom.Do we reject the null hypothesis at the 5% significance level?

Question 37

Researchers at a car resale company are trying to build a model to predict a car's 4-year resale value (in thousands of dollars)from several predictor variables.The variables they selected are as below. Data were collected on cars of different models made by different manufacturers.SPSS output for the least-squares regression model is given below. What is the equation of the least-squares regression line?

Question 38

Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. What is the value of an estimate of ²?

A)3.4369
B)11.813
C)543.379
D)1526.645

Question 39

Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. Suppose we wish to test the hypotheses H₀: ₁ = ₂ = 0 versus H_a: at least one of the _j is not 0,using the ANOVA F test.What is the value of the test statistic?

A)-11.379
B)-4.230
C)10.912
D)129.239

Question 40

Researchers at a car resale company are trying to build a model to predict a car's 4-year resale value (in thousands of dollars)from several predictor variables.The variables they selected are as below. Data were collected on cars of different models made by different manufacturers.SPSS output for the least-squares regression model is given below. What is the value of an estimate for the error standard deviation ?

Question 41

The NFL keeps track of a large number of statistics during the football season.For 2009 the number of points scored per game and how it related to such variables as the number of passes attempted per game (PassAtt/G),the total pass yards gained during the season (PassYds),and the total rushing yards gained in the season (RushYds)were studied.The following tables provide information on the least-squares fit of a multiple regression model for Pts/G on the three explanatory variables. What would be the 96% confidence interval estimate for the true regression coefficient for the variable PassAtt/G?

A)(-0.080,0.001)
B)(-1.025,0.007)
C)(-0.007,1.025)
D)(-5.203,4.185)
E)Not within ± 0.02 of any of the above

Question 42

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. What are the explanatory variables in this study?

A)Gender and Bart score
B)Gender and PPI
C)Gender,heroin,and PPI

Question 43

A study was conducted on 40 different brands of golf balls with respect to the distance the ball traveled after being struck with standardized test 7-iron.The response variable DIST is the measurement of the carry distance of the shot in yards.The explanatory variables are SMASH,the ratio of the ball speed/club speed at impact;SPIN,the initial spin rate of the ball in RPMs;and HEIGHT,the peak height of the ball in flight measured in feet. The following is a table showing some computer output (missing results are shown by _**)for a least-squares fit of a multiple regression model using these variables. What is the value of the squared multiple correlation ?

A)0.036
B)0.960
C)0.163
D)0.964
E)0.404

Question 44

A study was conducted on 40 different brands of golf balls with respect to the distance the ball traveled after being struck with standardized test 7-iron.The response variable DIST is the measurement of the carry distance of the shot in yards.The explanatory variables are SMASH,the ratio of the ball speed/club speed at impact;SPIN,the initial spin rate of the ball in RPMs;and HEIGHT,the peak height of the ball in flight measured in feet. The following is a table showing some computer output (missing results are shown by _**)for a least-squares fit of a multiple regression model using these variables. Based upon the P-value of the ANOVA F test,what can be concluded about the relationship between the response variable and the explanatory variables?

A)A significant amount of the variation in the response variable can be explained by the regression on the explanatory variables.
B)There is strong evidence that the distance a golf ball travels depends upon the variable SMASH.
C)There is strong statistical evidence that at least one of the regression coefficients is not equal to zero.
D)When considered on its own,the variable SPIN is significantly different from zero.
E)There is strong statistical evidence that none of the regression coefficients is equal and all are significantly different from zero.

Question 45

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. What proportion of the variation of the response variable is explained by the explanatory variables?

A)4.48%
B)20%
C)2%
D)40%

Question 46

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. Based on this model,are heroin users bigger risktakers than non-heroin users?

A)Yes
B)No

Question 47

Data were obtained in a study of the oxygen uptake of 31 middle-aged-males and females while exercising.The researchers were interested in the use of a variety of variables as predictors of Oxygen Uptake.The variables that were measured on the subjects were Age,Weight,the time taken to run a specified distance (Runtime),pulse rate at the end of the run (RunPulse),their resting pulse rate (RstPulse),and their maximum pulse rate during the run (MaxPulse).The following table from a computer analysis of the data is provided (with some entries deleted and replaced by _**). What is the mean square for model (MSM)?

A)144.293
B)120.244
C)721.463
D)180.366
E)141.897

Question 48

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. Does this model seem like an adequate model to predict risk-taking propensity?

A)No,the R-squared value is very low and most of the variables are not statistically significant.
B)Yes,the r correlation is very strong.
C)This cannot be determined from the given information.

Question 49

The NFL keeps track of a large number of statistics during the football season.For 2009 the number of points scored per game and how it related to such variables as the number of passes attempted per game (PassAtt/G),the total pass yards gained during the season (PassYds),and the total rushing yards gained in the season (RushYds)were studied.The following tables provide information on the least-squares fit of a multiple regression model for Pts/G on the three explanatory variables. If a team were to attempt 30 passes per game,pass for a total of 3500 yards,and rush for 2000 yards,what would the fitted regression model predict for the points the team would score per game?

A)25.2
B)27.6
C)44.9
D)58.2
E)18.8

Question 50

Data were obtained in a study of the oxygen uptake of 31 middle-aged-males and females while exercising.The researchers were interested in the use of a variety of variables as predictors of Oxygen Uptake.The variables that were measured on the subjects were Age,Weight,the time taken to run a specified distance (Runtime),pulse rate at the end of the run (RunPulse),their resting pulse rate (RstPulse),and their maximum pulse rate during the run (MaxPulse).The following table from a computer analysis of the data is provided (with some entries deleted and replaced by _**). What is the value of the F statistic and the associated degrees of freedom for the test?

A)F = 5.55 and DF = 6,30
B)F = 5.55 and DF = 6,24
C)F = 22.21 and DF = 6,30
D)F = 22.21 and DF = 5,24
E)F = 22.21 and DF = 6,24

Question 51

Which of the following statements about the statistical model for multiple linear regression, ,i = 1,2,…,n,is/are FALSE?

A)The deviations are independent.
B)The mean response is a linear function of the explanatory variables .
C)The parameters of the model are ,p,and .
D)The deviations are Normally distributed with a mean of 0 and a standard deviation of .
E)The deviations are a simple random sample from the N(0,)distribution.

Question 52

Data were obtained in a study of the oxygen uptake of 31 middle-aged-males and females while exercising.The researchers were interested in the use of a variety of variables as predictors of Oxygen Uptake.The variables that were measured on the subjects were Age,Weight,the time taken to run a specified distance (Runtime),pulse rate at the end of the run (RunPulse),their resting pulse rate (RstPulse),and their maximum pulse rate during the run (MaxPulse).The following table from a computer analysis of the data is provided (with some entries deleted and replaced by _**). Under H₀: against H_a: to test the significance of the variable Weight,what are the values of the test statistic and the P-value of the test?

A)t = 1.36 and the P-value is between 0.1 and 0.2.
B)t = -1.36 and the P-value is between 0.05 and 0.1.
C)t = -1.36 and the P-value is between 0.1 and 0.2.
D)t = -1.36 and the P-value is greater than 0.2.
E)t = 1.36;and the P-value is between 0.05 and 0.1.

Question 53

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. What is the response variable in this study?

A)Gender and Bart score
B)BART score
C)Gender and PPI
D)Gender,heroin,and PPI

Question 54

Data were obtained in a study of the oxygen uptake of 31 middle-aged-males and females while exercising.The researchers were interested in the use of a variety of variables as predictors of Oxygen Uptake.The variables that were measured on the subjects were Age,Weight,the time taken to run a specified distance (Runtime),pulse rate at the end of the run (RunPulse),their resting pulse rate (RstPulse),and their maximum pulse rate during the run (MaxPulse).The following table from a computer analysis of the data is provided (with some entries deleted and replaced by _**). What would the appropriate hypotheses be for testing the regression coefficients using the F ratio in the above table?

A)H₀:
H_a:

B)H₀:
H_a: at least one of the
is not 0
C)H₀:
H_a:

D)H₀: all the = 0
H_a: all the
 0
E)H₀: at most all of the = 0
H_a: at least one or more of the
= 0

Question 55

Data were obtained in a study of the oxygen uptake of 31 middle-aged-males and females while exercising.The researchers were interested in the use of a variety of variables as predictors of Oxygen Uptake.The variables that were measured on the subjects were Age,Weight,the time taken to run a specified distance (Runtime),pulse rate at the end of the run (RunPulse),their resting pulse rate (RstPulse),and their maximum pulse rate during the run (MaxPulse).The following table from a computer analysis of the data is provided (with some entries deleted and replaced by _**). In the above computer output we note that the t ratio for the variable RunPulse is -3.04,with a P-value of 0.0056.What is the best interpretation of this result?

A)The small P-value suggests that the variable RunPulse is not a significant predictor of Oxygen Uptake.
B)There is strong evidence that RunPulse is an important variable.
C)When assessing the value of variables for predicting Oxygen Uptake,the variable RunPulse by itself is very important.
D)The small P-value suggests that the variable RunPulse is statistically significant when all the other predictor variables are included in the regression equation.
E)The regression equation should include RunPulse since it is a statistically significant variable.

Question 56

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. Based on this model,are men bigger risktakers than women?

A)Yes
B)No

Question 57

In this experiment,the risk-taking propensity of 90 inner city drug users was measured using a repeated measures test called the Behavioral Analogue Risk Task (BART;Lejuez et al. ,2002).The higher the BART score,the higher the risk-taking propensity.Participants also filled out questionnaires so that their Psychopathic Personality Inventory (PPI)scores could be computed.PPI scores are used to detect psychopathic traits in a covert manner and are a common indicator of one's level of psychopathy.The main goal of the experiment was to examine the relationship between risk-taking (measured by BART)based on one's level of psychopathy (measured by PPI on a scale of 0-100),gender (1 for male and 2 for female),and heroin use (1 for heroin use and 0 for no heroin use).Below is a partial output of a multiple regression analysis. How many explanatory variables are in this study?

A)One
B)Two
C)Three

Question 58

A study was conducted on 40 different brands of golf balls with respect to the distance the ball traveled after being struck with standardized test 7-iron.The response variable DIST is the measurement of the carry distance of the shot in yards.The explanatory variables are SMASH,the ratio of the ball speed/club speed at impact;SPIN,the initial spin rate of the ball in RPMs;and HEIGHT,the peak height of the ball in flight measured in feet. The following is a table showing some computer output (missing results are shown by _**)for a least-squares fit of a multiple regression model using these variables. What is the estimate of the parameter ?

A)0.404
B)0.163
C)51.885
D)7.203
E)4.141

Question 59

Data were obtained in a study of the oxygen uptake of 31 middle-aged-males and females while exercising.The researchers were interested in the use of a variety of variables as predictors of Oxygen Uptake.The variables that were measured on the subjects were Age,Weight,the time taken to run a specified distance (Runtime),pulse rate at the end of the run (RunPulse),their resting pulse rate (RstPulse),and their maximum pulse rate during the run (MaxPulse).The following table from a computer analysis of the data is provided (with some entries deleted and replaced by _**). The degrees of freedom for model (DFM)and total (DFT)are

A)DFM = 5 and DFT = 31.
B)DFM = 4 and DFT = 30.
C)DFM = 6 and DFT = 31.
D)DFM = 6 and DFT = 30.
E)DFM = 5 and DFT = 30.

Question 60

What is the major difference between a simple linear regression model and a multiple linear regression model?

A)In simple linear regression you can only have quantitative explanatory variables.In multiple linear regression you can have quantitative and categorical explanatory variables.
B)In simple linear regression you have many explanatory variables.In multiple linear regression you have only one explanatory variable.
C)In simple linear regression you have only one explanatory variable.In multiple linear regression you can have many explanatory variables.

Question 61

Many people believe that parents' marital status influences their child's development throughout life and has a large effect on their child's skill in sports.A survey was sent to 100 students who were in athletics in college.Responses from 35 students were received.The researchers were interested in determining whether the marital status and level of happiness of the students' parents would predict the student's self-rated skill level in a sport.The test statistic used to test the null hypothesis that parents' marital status and level of happiness do not have an impact on a students' skill level in a sport is based on what distribution?

A)F
B)T
C)Normal
D)Binomial

Question 62

A multiple linear regression model can be described by DATA = FIT + RESIDUAL.What does the FIT part represent?

A)The parameters of the model
B)The subpopulation means
C)The variation of observations about the means
D)None of the above

Question 63

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. Examine the Q-Q plot of the residuals.What do you notice?

A)The Q-Q plot indicates some deviations from Normality,which could invalidate the analyses.
B)The residuals appear Normal;therefore,the regression results are accurate.
C)The residuals should be checked using a boxplot instead of a Q-Q plot.Not enough information can be obtained from the Q-Q plot.
D)One cannot obtain any information about the model from the residuals.

Question 64

Many people believe that parents' marital status influences their child's development throughout life and has a large effect on their child's skill in sports.A survey was sent to 100 students who were in athletics in college.Responses from 35 students were received.The researchers were interested in determining whether the marital status and level of happiness of the students' parents would predict the student's self-rated skill level in a sport.What is the number of cases?

A)100
B)35
C)4
D)None of the above

Question 65

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. Observe the table for the descriptive statistics.Which of the variables has a value that is more than 3 standard deviations from the mean?

A)Age
B)Married
C)Liquor
D)This cannot be determined from the information given.

Question 66

What is a multiple correlation coefficient?

A)A measure of the correlation between the observations y_i and the predicted values
B)The proportion of the variation of the response variable that is explained by the explanatory variables
C)The parameters in a multiple regression model
D)None of the above

Question 67

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. What should be done to examine the relationship between every pair of variables more closely?

A)Examine the 36 scatterplots that represent every pairwise relationship.
B)Examine the 26 scatterplots that represent every pairwise relationship.
C)Examine side-by-side boxplots of all the 9 variables in the model.
D)Examine a histogram of all the 9 variables in the model.

Question 68

A multiple linear regression model can be described by DATA = FIT + RESIDUAL.What does the RESIDUAL part represent?

A)The parameters of the model
B)The subpopulation means
C)The variation of observations about the means
D)None of the above

Question 69

In multiple regression,what does the parameter ² measure?

A)The variability of the responses about the population regression equation
B)The degrees of freedom associated with s²
C)The subpopulation means
D)None of the above

Question 70

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. Preliminary analysis indicated that the independent variable,Greek,was clearly not normal and skewed left.Will this cause any problems with the results of the regression analysis?

A)Yes,all of the variables in a regression model need to be normal.
B)Yes,however performing a transformation of the variable Greek that results in a normally distributed distribution will fix the problem.
C)No,there are no distribution assumptions for the independent variables in a regression analysis.
D)No,only in simple linear regression does the independent variable need to be normally distributed.

Question 71

Multiple regression can be used for which of the following?

A)Prediction
B)Extrapolation
C)All of the above
D)None of the above

Question 72

Suppose you want to perform a multiple linear regression analysis on data.You survey several students on campus and ask them a few questions.Which format below would you use to enter the data into a software program?

A)
B)

Question 73

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. The explanatory variables tuition,age,and liquor not highly corrected with crime.Does that mean they should not be in the model?

A)Yes,because only variables that are highly correlated with the response variable will be significant predictors in a regression analysis.
B)No.Just because a variable is not correlated with the response variable does not imply it will not be a statistically significant predictor.
C)No,because as long the correlation coefficient is large enough,that variable will be a significant predictor in a regression model.
D)Yes.Only in simple linear regression would variables that are not highly correlated with the response variable be statistically significant predictors in a regression model.

Question 74

Many people believe that parents' marital status influences their child's development throughout life and has a large effect on their child's skill in sports.A survey was sent to 100 students who were in athletics in college.Responses from 35 students were received.The researchers were interested in determining whether the marital status and level of happiness of the students' parents would predict the student's self-rated skill level in a sport.The statistical model for the multiple linear regression is in the form of which of the following? (Note: assume i = 1 to n,where n is the number of cases. )

A)
B)
C)
D)

Question 75

Many people believe that parents' marital status influences their child's development throughout life and has a large effect on their child's skill in sports.A survey was sent to 100 students who were in athletics in college.Responses from 35 students were received.The researchers were interested in determining whether the marital status and level of happiness of the students' parents would predict the student's self-rated skill level in a sport.What is/are the explanatory variables in this study?

A)Skill level in a sport
B)Marital status
C)Level of happiness
D)B and C

Question 76

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. Does the response variable,crime,meet the assumption necessary for the analysis?

A)Yes,the response variable appears perfectly normal.
B)No,the Q-Q plot shows slight curvatures which may indicate the data are skewed.
C)You cannot tell from the information provided.
D)There are no assumptions for the response variable for a regression analysis.

Question 77

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. What type of statistical analysis was used on these data?

A)Simple linear regression
B)Multiple linear regression
C)Logistic regression
D)Categorical data analysis

Question 78

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. The ANOVA F statistic is 1.642 with a P-value of .130.What does this tell us about the regression coefficients for the explanatory variables?

A)At least one of the regression coefficients is different from zero in the population regression equation.
B)All of the regression coefficients are different from zero in the population regression equation.
C)None of the regression coefficients are different from zero in the population regression equation.

Question 79

Many people believe that parents' marital status influences their child's development throughout life and has a large effect on their child's skill in sports.A survey was sent to 100 students who were in athletics in college.Responses from 35 students were received.The researchers were interested in determining whether the marital status and level of happiness of the students' parents would predict the student's self-rated skill level in a sport.What is the response variable in this study?

A)Skill level in a sport
B)Marital status
C)Level of happiness
D)B and C

Question 80

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. Does the significance test for the individual regression coefficients for marriage and income contradict the information we obtained from the correlation table?

A)Yes,both marriage and income are correlated with crime and the correlation is statistically significant.Therefore,something is wrong with the regression analysis.
B)No,marriage and income are both highly correlated with each other.Therefore,there is likely a significant overlap of the predictive information from these variables.