Question 1

A multiple regression model has the form:   . As x2 increases by one unit, holding x1 constant, then the value of y will increase by:

Accepted Answer

A)  7.25 units 
B)  6 units on average 
C)  2 units 
D)  None of these choices 
A)  7.25 units 
B)  6 units on average 
C)  2 units 
D)  None of these choices

Question 2

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

Accepted Answer

A)  F-test 
B)  t-test 
C)  z-test 
D)  None of these choices. 
A)  F-test 
B)  t-test 
C)  z-test 
D)  None of these choices.

Question 3

A multiple regression model has the form   . The coefficient b1 is interpreted as the average change in y per unit change in x1.

Accepted Answer

A) True 
 B)False

Question 4

Student's Final Grade: A statistics professor investigated some of the factors that affect an individual student's final grade in her course. She proposed the multiple regression model   , where y is the final grade (out of 100 points), xS1U1B11S1U1B0 is the number of lectures skipped, xS1U1B12S1U1B0 is the number of late assignments, and xS1U1B13S1U1B0 is the midterm exam score (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below.
THE REGRESSION EQUATION IS       ANALYSIS OF VARIANCE
  
-Interpret the coefficient b1.

Accepted Answer

b₁ = -3.18. This tells us tha

Question 5

Life Expectancy
An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week (xS1U1B11S1U1B0), the cholesterol level (xS1U1B12S1U1B0), and the number of points that the individual's blood pressure exceeded the recommended value (xS1U1B13S1U1B0). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below.
THE REGRESSION EQUATION IS
y = 55.8 + 1.79xS1U1B11S1U1B0 -0.021xS1U1B12S1U1B0 - 0.061xS1U1B13S1U1B0
     ANALYSIS OF VARIANCE
  
-{Life Expectancy Narrative} Is there sufficient evidence at the 5% significance level to infer that the number of points that the individual's blood pressure exceeded the recommended value and the age at death are negatively linearly related?

Accepted Answer

@#IMG-DLM& vs. @#IMG-DLM& Rejection region: t < -t<sub>0.05,

Question 6

The coefficient of determination R2 measures the proportion of variation in y that is explained by the explanatory variables included in the model.

Accepted Answer

A) True 
 B)False

Question 7

In reference to the equation   , the value 0.12 is the average change in y per unit change in x1, when x2 is held constant.

Accepted Answer

A) True 
 B)False

Question 8

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is   .

Accepted Answer

A) True 
 B)False

Question 9

In a multiple regression analysis involving 40 observations and 5 independent variables, the following statistics are given: Total variation in y = 350 and SSE = 50. Then, the coefficient of determination is:

Accepted Answer

A)  0.8408 
B)  0.8571 
C)  0.8469 
D)  0.8529 
A)  0.8408 
B)  0.8571 
C)  0.8469 
D)  0.8529

Question 10

A multiple regression equation has a coefficient of determination of 0.81. Then, the percentage of the variation in y that is explained by the regression equation is 90%.

Accepted Answer

A) True 
 B)False

Question 11

Use the residuals to compute the standardized residuals.

Accepted Answer

The standardized res

Question 12

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s $\varepsilon$  are both small, the coefficient of determination R2 is close to 1, and the value of the test statistic F is large.

Accepted Answer

A) True 
 B)False

Question 13

A multiple regression model involves 10 independent variables and 30 observations. If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. $\neq$ 0) the critical value will be:

Accepted Answer

A)  2.228 
B)  2.093 
C)  1.729 
D)  1.697 
A)  2.228 
B)  2.093 
C)  1.729 
D)  1.697

Question 14

The validity of a multiple regression model is tested using a(n) _________ test.

Accepted Answer

The answer of The validity of a multiple regression model...

Question 15

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Accepted Answer

A) True 
 B)False

Question 16

A high correlation between two independent variables is an indication of ____________________.

Accepted Answer

The answer of A high correlation between two independent variables...

Question 17

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Accepted Answer

A) True 
 B)False

Question 18

For a multiple regression model, the following statistics are given: Total variation in y = 500, SSE = 80, and n = 25. Then, the coefficient of determination is:

Accepted Answer

A)  0.84 
B)  0.16 
C)  0.3125 
D)  0.05 
A)  0.84 
B)  0.16 
C)  0.3125 
D)  0.05

Question 19

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:

Accepted Answer

A)  heteroscedasticity. 
B)  an error in the analysis. 
C)  multicollinearity. 
D)  None of these choices. 
A)  heteroscedasticity. 
B)  an error in the analysis. 
C)  multicollinearity. 
D)  None of these choices.

Question 20

Use the regression equation   to determine the predicted values of y.

Accepted Answer

The predic

A multiple regression model has the form: . As x₂ increases by one unit, holding x₁ constant, then the value of y will increase by:

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

A multiple regression model has the form . The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

The coefficient of determination R² measures the proportion of variation in y that is explained by the explanatory variables included in the model.

In reference to the equation , the value 0.12 is the average change in y per unit change in x₁, when x₂ is held constant.

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is .

In a multiple regression analysis involving 40 observations and 5 independent variables, the following statistics are given: Total variation in y = 350 and SSE = 50. Then, the coefficient of determination is:

A multiple regression equation has a coefficient of determination of 0.81. Then, the percentage of the variation in y that is explained by the regression equation is 90%.

Use the residuals to compute the standardized residuals.

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both small, the coefficient of determination R² is close to 1, and the value of the test statistic F is large.

A multiple regression model involves 10 independent variables and 30 observations. If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. $\neq$ 0) the critical value will be:

The validity of a multiple regression model is tested using a(n) _________ test.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

A high correlation between two independent variables is an indication of ____________________.

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

For a multiple regression model, the following statistics are given: Total variation in y = 500, SSE = 80, and n = 25. Then, the coefficient of determination is:

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:

Use the regression equation to determine the predicted values of y.

What Is Statistics

Graphical and Tabular Descriptive Techniques

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations, Part 1

Inference About Comparing Two Populations, Part 2

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Review of Statistical Inference

Filters

Exam 17: Multiple Regression

A multiple regression model has the form: . As x2 increases by one unit, holding x1 constant, then the value of y will increase by:

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

A multiple regression model has the form . The coefficient b1 is interpreted as the average change in y per unit change in x1.

The coefficient of determination R2 measures the proportion of variation in y that is explained by the explanatory variables included in the model.

In reference to the equation , the value 0.12 is the average change in y per unit change in x1, when x2 is held constant.

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is .

In a multiple regression analysis involving 40 observations and 5 independent variables, the following statistics are given: Total variation in y = 350 and SSE = 50. Then, the coefficient of determination is:

A multiple regression equation has a coefficient of determination of 0.81. Then, the percentage of the variation in y that is explained by the regression equation is 90%.

Use the residuals to compute the standardized residuals.

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s ε\varepsilonε are both small, the coefficient of determination R2 is close to 1, and the value of the test statistic F is large.

A multiple regression model involves 10 independent variables and 30 observations. If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. ≠\neq= 0) the critical value will be:

The validity of a multiple regression model is tested using a(n) _________ test.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

A high correlation between two independent variables is an indication of ____________________.

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

For a multiple regression model, the following statistics are given: Total variation in y = 500, SSE = 80, and n = 25. Then, the coefficient of determination is:

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:

Use the regression equation to determine the predicted values of y.

What Is Statistics

Graphical and Tabular Descriptive Techniques

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations, Part 1

Inference About Comparing Two Populations, Part 2

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Review of Statistical Inference

Filters

A multiple regression model has the form: . As x₂ increases by one unit, holding x₁ constant, then the value of y will increase by:

A multiple regression model has the form . The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

The coefficient of determination R² measures the proportion of variation in y that is explained by the explanatory variables included in the model.

In reference to the equation , the value 0.12 is the average change in y per unit change in x₁, when x₂ is held constant.

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both small, the coefficient of determination R² is close to 1, and the value of the test statistic F is large.

A multiple regression model involves 10 independent variables and 30 observations. If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. $\neq$ 0) the critical value will be: