Question 1

If all the points for a multiple regression model with two independent variables were right on the regression plane, then the coefficient of determination would equal:

Accepted Answer

A) 0. 
B) 1. 
C) 2, since there are two independent variables. 
D) None of these choices. 
A) 0. 
B) 1. 
C) 2, since there are two independent variables. 
D) None of these choices.

Question 2

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

Accepted Answer

The answer of The coefficient of determination ____________________ for degrees...

Question 3

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Accepted Answer

A) True 
 B)False

Question 4

How do you go about checking for multicollinearity?

Accepted Answer

A practical way to identify multicolline

Question 5

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

Accepted Answer

A) True 
 B)False

Question 6

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Accepted Answer

A) True 
 B)False

Question 7

A multiple regression model has the form $\hat { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }$ . As x3 increases by one unit, with x1 and x2 held constant, the y on average is expected to:

Accepted Answer

A) increase by 1 unit. 
B) increase by 12 units. 
C) decrease by 4 units. 
D) decrease by 16 units. 
A) increase by 1 unit. 
B) increase by 12 units. 
C) decrease by 4 units. 
D) decrease by 16 units.

Question 8

Most statistical software print a second R2 statistic, called the coefficient of determination adjusted for degrees of freedom, which has been adjusted to take into account the sample size and the number of independent variables.

Accepted Answer

A) True 
 B)False

Question 9

NARRBEGIN: Life Expectancy
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
 $$\begin{array} { | c | c c c | } 
\hline \text { predictor } & Coef  & SUDev  & T \
\hline \text { Constant } & 55.8 & 11.8 & 4.729 \
\boldsymbol { \lambda } _ { 1 } & 1.79 & 0.44 & 4.068 \
\lambda _ { 2 } & - 0.021 & 0.011 & - 1.909 \
\lambda _ { 3 } & - 0.016 & 0.014 & - 1.143 \
\hline
\end{array}$$ $$S = 9.47 \quad R - S q = 22.5 \%$$ ANALYSIS OF VARIANCE
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \boldsymbol { d } & \mathbf { SS } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Repression } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Tatol } & 39 & 4166 & & \
\hline
\end{array}$$ NARREND
-{Life Expectancy Narrative} Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life?

Accepted Answer

@#LAT-DLM& @#LAT-DLM& At least one @#LAT-DLM&_i is not equal to zero.Rej

Question 10

A multiple regression model has the form: $\hat { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }$ . 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 11

When there is more than one independent variable in a regression model, we refer to the graphical depiction of the equation as a(n) ____________________ rather than as a straight line.

Accepted Answer

The answer of When there is more than one independent...

Question 12

In a multiple regression model, the standard deviation of the error variable$\varepsilon$is assumed to be:

Accepted Answer

A) 0. 
B) 1.0. 
C) constant. 
D) None of these choices. 
A) 0. 
B) 1.0. 
C) constant. 
D) None of these choices.

Question 13

When an explanatory variable is dropped from a multiple regression model, the coefficient of determination can increase.

Accepted Answer

A) True 
 B)False

Question 14

NARRBEGIN: Life Expectancy
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
 $$\begin{array} { | c | c c c | } 
\hline \text { predictor } & Coef  & SUDev  & T \
\hline \text { Constant } & 55.8 & 11.8 & 4.729 \
\boldsymbol { \lambda } _ { 1 } & 1.79 & 0.44 & 4.068 \
\lambda _ { 2 } & - 0.021 & 0.011 & - 1.909 \
\lambda _ { 3 } & - 0.016 & 0.014 & - 1.143 \
\hline
\end{array}$$ $$S = 9.47 \quad R - S q = 22.5 \%$$ ANALYSIS OF VARIANCE
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \boldsymbol { d } & \mathbf { SS } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Repression } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Tatol } & 39 & 4166 & & \
\hline
\end{array}$$ NARREND
-{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

@#LAT-DLM& vs. @#LAT-DLM& Rejection region: t < -t_0.05,36@#LAT-DLM& -1.69 Tes

Question 15

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 16

The coefficient of determination ranges from:

Accepted Answer

A) 1.0 to $\infty$. 
B) 0.0 to 1.0. 
C) 1.0 to k, where k is the number of independent variables in the model. 
D) 1.0 to n, where n is the number of observations in the dependent variable. 
A) 1.0 to $\infty$. 
B) 0.0 to 1.0. 
C) 1.0 to k, where k is the number of independent variables in the model. 
D) 1.0 to n, where n is the number of observations in the dependent variable.

Question 17

Test the hypotheses H0: no first-order autocorrelation vs. H1: first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.89, n = 28, k = 3, and $\alpha$ = 0.05.

Accepted Answer

d_L = 0.97 and d_U = 1.41 The decision is ma

Question 18

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

Accepted Answer

A) True 
 B)False

Question 19

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

Accepted Answer

A) True 
 B)False

Question 20

Large values of the Durbin-Watson statistic d (d > 2) indicate a positive first-order autocorrelation.

Accepted Answer

A) True 
 B)False

If all the points for a multiple regression model with two independent variables were right on the regression plane, then the coefficient of determination would equal:

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

How do you go about checking for multicollinearity?

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

A multiple regression model has the form $\hat { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }$ . As x₃ increases by one unit, with x₁ and x₂ held constant, the y on average is expected to:

Most statistical software print a second R² statistic, called the coefficient of determination adjusted for degrees of freedom, which has been adjusted to take into account the sample size and the number of independent variables.

A multiple regression model has the form: $\hat { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }$ . As x₂ increases by one unit, holding x₁ constant, then the value of y will increase by:

When there is more than one independent variable in a regression model, we refer to the graphical depiction of the equation as a(n) ____________________ rather than as a straight line.

In a multiple regression model, the standard deviation of the error variable $\varepsilon$ is assumed to be:

When an explanatory variable is dropped from a multiple regression model, the coefficient of determination can increase.

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:

The coefficient of determination ranges from:

Test the hypotheses H₀: no first-order autocorrelation vs. H₁: first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.89, n = 28, k = 3, and $\alpha$ = 0.05.

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

Large values of the Durbin-Watson statistic d (d > 2) indicate a positive first-order autocorrelation.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

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

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Filters

Exam 17: Multiple Regression

If all the points for a multiple regression model with two independent variables were right on the regression plane, then the coefficient of determination would equal:

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

How do you go about checking for multicollinearity?

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

A multiple regression model has the form y^=8+3x1+5x2−4x3\hat { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }y^​=8+3x1​+5x2​−4x3​ . As x3 increases by one unit, with x1 and x2 held constant, the y on average is expected to:

Most statistical software print a second R2 statistic, called the coefficient of determination adjusted for degrees of freedom, which has been adjusted to take into account the sample size and the number of independent variables.

A multiple regression model has the form: y^=5.25+2x1+6x2\hat { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }y^​=5.25+2x1​+6x2​ . As x2 increases by one unit, holding x1 constant, then the value of y will increase by:

When there is more than one independent variable in a regression model, we refer to the graphical depiction of the equation as a(n) ____________________ rather than as a straight line.

In a multiple regression model, the standard deviation of the error variable ε\varepsilonε is assumed to be:

When an explanatory variable is dropped from a multiple regression model, the coefficient of determination can increase.

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:

The coefficient of determination ranges from:

Test the hypotheses H0: no first-order autocorrelation vs. H1: first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.89, n = 28, k = 3, and α\alphaα = 0.05.

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

Large values of the Durbin-Watson statistic d (d > 2) indicate a positive first-order autocorrelation.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

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

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Filters

A multiple regression model has the form $\hat { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }$ . As x₃ increases by one unit, with x₁ and x₂ held constant, the y on average is expected to:

Most statistical software print a second R² statistic, called the coefficient of determination adjusted for degrees of freedom, which has been adjusted to take into account the sample size and the number of independent variables.

A multiple regression model has the form: $\hat { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }$ . As x₂ increases by one unit, holding x₁ constant, then the value of y will increase by:

In a multiple regression model, the standard deviation of the error variable $\varepsilon$ is assumed to be:

Test the hypotheses H₀: no first-order autocorrelation vs. H₁: first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.89, n = 28, k = 3, and $\alpha$ = 0.05.