A member of the provincial legislature has expressed concern about the differences in the mathematics test scores of grade 9 high school students across the province.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the province and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers \[\begin{array} { l c c } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.178 & 7.595 \\ \text { Math Dgr } & 0.22073 & 0.07131 \\ \text { Age } & 0.3353 & 0.1901 \\ \text { Salary } & 0.0930 & 0.1675 \end{array}\] s = 7.62090 Analysis of Variance \[\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \\ \text { Regression } & 3 & 1053.09 \\ \text { Residual Error } & 32 & 1858.50 \end{array}\] \[\begin{array} { l c c } \text { Source } & \text { DF } & \text { Seq SS } \\ \text { Math Dgr } & 1 & 672.10 \\ \text { Age } & 1 & 363.09 \\ \text { Salary } & 1 & 17.90 \end{array}\] Additional information related to this point estimate of 65.12 is given below. Predicted Values for New Observations 50% with math degree,average age of 43 and average salary is 48.3 New \[\begin{array} { c c c } \text { Obs } & \text { Fit Standard } & \text { Deviation Fit } \\ 1 & 65.12 & 1.68 \end{array}\] -Calculate the 95% prediction interval for this point estimate.

49.22 to 81.02 t .025,32 = 2.036 Dista

Below is a partial multiple regression ANOVA table. \[\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\ \mathrm { X } _ { 1 } & 535.9569 & 1 \\ \mathrm { X } _ { 2 } & 1,167.5634 & 1 \\ \mathrm { X } _ { 3 } & 18.9886 & 1 \\ \text { Error } & 3,459.6803 & 8 \end{array}\] -How many observations were in the sample?

A) 8 B) 10 C) 11 D) 12 E) 14 A) 8 B) 10 C) 11 D) 12 E) 14

Consider the following partial computer output for a multiple regression model. $\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\ \text { Constant } & 99.3883 & \\ \text { X1 } & - 0.007207 & 0.0031 \\ \mathrm { X } 2 & 0.0011336 & 0.00122 \\ \mathrm { X } 3 & 0.9324 & 0.373 \end{array}$ The calculated value of the t statistic for X1 is ________.

The answer of Consider the following partial computer output for...

The 95% confidence interval for β1 is from -0.4089 to 2.0493.Interpret the meaning of this interval.

We are 95% confident that if advertising

In the quadratic regression model y = $\beta$ 0 + $\beta$ 1X + $\beta$ 2 X2 + $\varepsilon$ ,if the term $\beta$ 2 is ______ zero,then the parabola opens __________.

A) less than,upward B) greater than,upward C) greater than,either upward or downward D) less than,either upward or downward E) equal to,downward A) less than,upward B) greater than,upward C) greater than,either upward or downward D) less than,either upward or downward E) equal to,downward

Below is a partial multiple regression ANOVA table. \[\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\ \mathrm { X } _ { 1 } & 535.9569 & 1 \\ \mathrm { X } _ { 2 } & 1,167.5634 & 1 \\ \mathrm { X } _ { 3 } & 18.9886 & 1 \\ \text { Error } & 3,459.6803 & 8 \end{array}\] -What is the value of F?

A) 1.28 B) 3.28 C) 6.22 D) 1.33 E) 8.11 A) 1.28 B) 3.28 C) 6.22 D) 1.33 E) 8.11

Below is a partial multiple regression ANOVA table. \[\begin{array} { l l l } \text { Source } & \text { SS } & \text { df } \\ \mathrm { X } _ { 1 } & 535.9569 & 1 \\ \mathrm { X } _ { 2 } & 1,167.5634 & 1 \\ \mathrm { X } _ { 3 } & 18.9886 & 1 \\ \text { Error } & 3,459.6803 & 8 \end{array}\] -What is the proportion of the variation explained by the multiple regression model?

A) .53 B) .12 C) .18 D) .19 E) .33 A) .53 B) .12 C) .18 D) .19 E) .33

Consider the following partial computer output for a multiple regression model. \[\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\ \text { Constant } & 99.3883 & \\ \mathrm { X } 1 & - 0.007207 & 0.0031 \\ \mathrm { X } 2 & 0.0011336 & 0.00122 \\ \mathrm { X } 3 & 0.9324 & 0.373 \\ & & \\ \text { Analysis of Variance } & & \mathrm { SS } \\ \text { Source } & \underline { \text { df } } & 31.308 \\ \text { Regression } & 3 & 9.378 \\ \text { Error (residual) } & 16 & \end{array}\] -The calculated value of the t statistic for X1 is ________.

A) -3.100 B) -2.122 C) -7.207 D) -2.325 E) -9.324 A) -3.100 B) -2.122 C) -7.207 D) -2.325 E) -9.324

Exam 12: Multiple Regression and Model Building

A member of the provincial legislature has expressed concern about the differences in the mathematics test scores of grade 9 high school students across the province.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the province and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers Predictor Coef SE Coef Constant 35.178 7.595 Math Dgr 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 s = 7.62090 Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Math Dgr 1 672.10 Age 1 363.09 Salary 1 17.90 Additional information related to this point estimate of 65.12 is given below. Predicted Values for New Observations 50% with math degree,average age of 43 and average salary is 48.3 New Obs Fit Standard Deviation Fit 1 65.12 1.68 -Calculate the 95% prediction interval for this point estimate.

(Essay)

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Question 21

Due to the fact that multiple regression models consist of multiple independent variables,residual analysis cannot be performed.

(True/False)

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Question 22

Which of the following is not an assumption of the multiple linear regression model?

(Multiple Choice)

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Question 23

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -How many observations were in the sample?

(Multiple Choice)

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Question 24

At $\alpha$ = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

(Essay)

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Question 25

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 X1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 The calculated value of the t statistic for X1 is ________.

(Short Answer)

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Question 26

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 X1 -0.007207 0.0031 X2 0.0011336 0.00122 X3 0.9324 0.373 Analysis of Variance SS Source df 31.308 Regression 3 9.378 -Test the overall usefulness of the model at alpha =.01.Calculate F and make your decision.

(Essay)

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Question 27

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 1.081 1.353 -18.404 4.547 Analysis of Variance Source Regression 2 2270.11 Error (residual) 26 3585.75 -What is the explained variation?

(Essay)

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Question 28

The 95% confidence interval for β₁ is from -0.4089 to 2.0493.Interpret the meaning of this interval.

(Essay)

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Question 29

Based on the multiple regression model given above,if the percentage of employees with a university degree is 50.0,the average age is 43,and the average salary is 48,300 (48.3),the average job satisfaction score is estimated to be _____.

(Multiple Choice)

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Question 30

In the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁X + $\beta$ ₂ X² + $\varepsilon$ ,if the term $\beta$ 2 is zero,then the parabola opens ____.

(Multiple Choice)

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Question 31

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

(Multiple Choice)

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Question 32

In converting the residual to a studentized (standardized)residual for a given observation,the residual for the observation is divided by the __________.

(Short Answer)

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Question 33

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the value of F?

(Multiple Choice)

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Question 34

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the proportion of the variation explained by the multiple regression model?

(Multiple Choice)

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Question 35

Assuming a quadratic model was used,write the least squares prediction equation.

(Essay)

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Question 36

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 Analysis of Variance Source 31.308 Regression 3 9.378 Error (residual) 16 -The calculated value of the t statistic for X₁ is ________.

(Multiple Choice)

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Question 37

A(n)_____ represents a data point which is unusual with respect to the experimental region and/or which has a y-value which is not consistent with the regression equation.

(Multiple Choice)

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Question 38

In a multiple regression analysis,if the normal plot of the residuals approximately displays the shape of a ____________,then it can be concluded that the assumption of error term normality is not significantly violated.

(Multiple Choice)

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Question 39

_____ variation is the sum of explained variation plus the sum of unexplained variation.

(Short Answer)

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Question 40

Due to the fact that multiple regression models consist of multiple independent variables,residual analysis cannot be performed.

Which of the following is not an assumption of the multiple linear regression model?

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -How many observations were in the sample?

At $\alpha$ = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 X1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 The calculated value of the t statistic for X1 is ________.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 1.081 1.353 -18.404 4.547 Analysis of Variance Source Regression 2 2270.11 Error (residual) 26 3585.75 -What is the explained variation?

The 95% confidence interval for β₁ is from -0.4089 to 2.0493.Interpret the meaning of this interval.

Based on the multiple regression model given above,if the percentage of employees with a university degree is 50.0,the average age is 43,and the average salary is 48,300 (48.3),the average job satisfaction score is estimated to be _____.

In the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁X + $\beta$ ₂ X² + $\varepsilon$ ,if the term $\beta$ 2 is zero,then the parabola opens ____.

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

In converting the residual to a studentized (standardized)residual for a given observation,the residual for the observation is divided by the __________.

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the value of F?

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the proportion of the variation explained by the multiple regression model?

Assuming a quadratic model was used,write the least squares prediction equation.

A(n)_____ represents a data point which is unusual with respect to the experimental region and/or which has a y-value which is not consistent with the regression equation.

In a multiple regression analysis,if the normal plot of the residuals approximately displays the shape of a ____________,then it can be concluded that the assumption of error term normality is not significantly violated.

_____ variation is the sum of explained variation plus the sum of unexplained variation.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Exam 12: Multiple Regression and Model Building

Due to the fact that multiple regression models consist of multiple independent variables,residual analysis cannot be performed.

Which of the following is not an assumption of the multiple linear regression model?

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -How many observations were in the sample?

At α\alphaα = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 X1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 The calculated value of the t statistic for X1 is ________.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 1.081 1.353 -18.404 4.547 Analysis of Variance Source Regression 2 2270.11 Error (residual) 26 3585.75 -What is the explained variation?

The 95% confidence interval for β1 is from -0.4089 to 2.0493.Interpret the meaning of this interval.

Based on the multiple regression model given above,if the percentage of employees with a university degree is 50.0,the average age is 43,and the average salary is 48,300 (48.3),the average job satisfaction score is estimated to be _____.

In the quadratic regression model y = β\betaβ 0 + β\betaβ 1X + β\betaβ 2 X2 + ε\varepsilonε ,if the term β\betaβ 2 is ______ zero,then the parabola opens __________.

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

In converting the residual to a studentized (standardized)residual for a given observation,the residual for the observation is divided by the __________.

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the value of F?

Below is a partial multiple regression ANOVA table. Source SS df 535.9569 1 1,167.5634 1 18.9886 1 Error 3,459.6803 8 -What is the proportion of the variation explained by the multiple regression model?

Assuming a quadratic model was used,write the least squares prediction equation.

A(n)_____ represents a data point which is unusual with respect to the experimental region and/or which has a y-value which is not consistent with the regression equation.

In a multiple regression analysis,if the normal plot of the residuals approximately displays the shape of a ____________,then it can be concluded that the assumption of error term normality is not significantly violated.

_____ variation is the sum of explained variation plus the sum of unexplained variation.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

At $\alpha$ = .05 test to determine if at least one of the two new independent variables make a significant contribution to the multiple regression model.

The 95% confidence interval for β₁ is from -0.4089 to 2.0493.Interpret the meaning of this interval.

In the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁X + $\beta$ ₂ X² + $\varepsilon$ ,if the term $\beta$ 2 is zero,then the parabola opens ____.