Question 1

TABLE 14-11
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds). Two variables thought to affect weight loss are client's length of time on the weight loss program and time of session. These variables are described below:
  Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model:
  Partial output from Microsoft Excel follows:
Regression Statistics
  ANOVA
 
-Referring to Table 14-11, which of the following statements is supported by the analysis shown?

Accepted Answer

A)  There is sufficient evidence (at α = 0.05) of curvature in the relationship between weight-loss (Y) and months in program(X1). 
B)  There is sufficient evidence (at α = 0.05) to indicate that the relationship between weight-loss (Y) and months in program (X1) depends on session time. 
C)  There is sufficient evidence (at α = 0.10) to indicate that the session time (morning, afternoon, evening) affects weight-loss (Y). 
D)  There is insufficient evidence (at α = 0.10) to indicate that the relationship between weight-loss (Y) and months in program (X1) depends on session time.

Question 2

If we have taken into account all relevant explanatory factors, the residuals from a multiple regression should be random.

Accepted Answer

A) True 
 B)False

Question 3

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-4, what are the residual degrees of freedom that are missing from the output?

Accepted Answer

A)  3 
B)  46 
C)  49 
D)  50

Question 4

A regression had the following results: SST = 102.55, SSE = 82.04. It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

Accepted Answer

A) True 
 B)False

Question 5

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (XS1U1B11S1U1B0 = Age), experience in the field (XS1U1B12S1U1B0 = Exper), number of degrees (XS1U1B13S1U1B0 = Degrees), and number of previous jobs in the field (XS1U1B14S1U1B0 = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-8, the net regression coefficient of X₂ is ________.

Accepted Answer

The answer of TABLE 14-8
A financial analyst wanted to examine...

Question 6

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, he obtained an r2 value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

Accepted Answer

A)  2.8% 
B)  51.8% 
C)  72.6% 
D)  74.8%

Question 7

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (XS1U1B11S1U1B0 = Age), experience in the field (XS1U1B12S1U1B0 = Exper), number of degrees (XS1U1B13S1U1B0 = Degrees), and number of previous jobs in the field (XS1U1B14S1U1B0 = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-8, the estimate of the unit change in the mean of Y per unit change in X₄, taking into account the effects of the other 3 variables, is ________.

Accepted Answer

The answer of TABLE 14-8
A financial analyst wanted to examine...

Question 8

TABLE 14-5
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-5, what is the p-value for Wages?

Accepted Answer

A)  0.01 
B)  0.05 
C)  0.0001 
D)  None of the above.

Question 9

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?

Accepted Answer

A)  5.286 
B)  5.195 
C)  3.945 
D)  -1.509

Question 10

TABLE 14-7
The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-7, the department head wants to test H0 : β1 = β2 = 0. At a level of significance of 0.05, the null hypothesis is rejected.

Accepted Answer

A) True 
 B)False

Question 11

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (XS1U1B11S1U1B0), the amount of insulation in inches (XS1U1B12S1U1B0), the number of windows in the house (XS1U1B13S1U1B0), and the age of the furnace in years (XS1U1B14S1U1B0). Given below are the EXCEL outputs of two regression models.
Model 1
  Note: 2.96869E-05 = 2.96869×10S1U1P1-5S1S1P0
Model 2
  Note: 2.9036E-06 = 2.9036×10S1U1P1-6S1S1P0
-Referring to Table 14-6, what can we say about Model 1?

Accepted Answer

A)  The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs. 
B)  The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs. 
C)  The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs. 
D)  The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.

Question 12

TABLE 14-7
The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-7, the department head wants to use a t test to test for the significance of the coefficient of X1. At a level of significance of 0.05, the department head would decide that β1 ≠ 0.

Accepted Answer

A) True 
 B)False

Question 13

TABLE 14-15
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0= % Attendance, XS1U1B12S1U1B0= Salaries and XS1U1B13S1U1B0= Spending:
  Note:
 
-Referring to Table 14-15, which of the following is a correct statement?

Accepted Answer

A)  60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class, average teacher salary, and instructional spending per pupil. 
B)  60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class, average teacher salary, and instructional spending per pupil after adjusting for the number of predictors and sample size. 
C)  60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class holding constant the effect of average teacher salary, and instructional spending per pupil. 
D)  60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily average of the percentage of students attending class after adjusting for the effect of average teacher salary, and instructional spending per pupil.

Question 14

TABLE 14-15
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0= % Attendance, XS1U1B12S1U1B0= Salaries and XS1U1B13S1U1B0= Spending:
  Note:
 
-Referring to Table 14-15, which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

Accepted Answer

A)  H1 : β0 ≠ 0 
B)  H1 : β1 ≠ 0 
C)  H1 : β2 ≠ 0 
D)  H1 : β3 ≠ 0

Question 15

The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

Accepted Answer

A) True 
 B)False

Question 16

TABLE 14-10
You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information:
 
-Referring to Table 14-10, the regression sum of squares that is missing in the ANOVA table should be ________.

Accepted Answer

The answer of TABLE 14-10
You worked as an intern at...

Question 17

TABLE 14-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

Accepted Answer

A)  5.286 
B)  5.195 
C)  3.945 
D)  -1.509

Question 18

TABLE 14-8
A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (XS1U1B11S1U1B0 = Age), experience in the field (XS1U1B12S1U1B0 = Exper), number of degrees (XS1U1B13S1U1B0 = Degrees), and number of previous jobs in the field (XS1U1B14S1U1B0 = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output:
SUMMARY OUTPUT
Regression Statistics
  ANOVA
  
-Referring to Table 14-8, the F test for the significance of the entire regression performed at a level of significance of 0.01 leads to a rejection of the null hypothesis.

Accepted Answer

A) True 
 B)False

Question 19

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics ANOVA -Referring to Table 14-7, the department head decided to obtain a 95% confidence interval for β₁. The confidence interval is from ________ to ________.

Accepted Answer

The answer of TABLE 14-7
The department head of the accounting...

Question 20

TABLE 14-15
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0= % Attendance, XS1U1B12S1U1B0= Salaries and XS1U1B13S1U1B0= Spending:
  Note:
 
-Referring to Table 14-15, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one dollar increase in instructional spending per pupil on the mean percentage of students passing the proficiency test?

Accepted Answer

The answer of TABLE 14-15
The superintendent of a school district...

Exam 14: Introduction to Multiple Regression

If we have taken into account all relevant explanatory factors, the residuals from a multiple regression should be random.

A regression had the following results: SST = 102.55, SSE = 82.04. It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.