Question 1

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of _____ variables.

Accepted Answer

qualitative or categorical

Question 2

The manufacturer of a light fixture believes that the dollars spent on advertising,the price of the fixture,and the number of retail stores selling the fixture in a particular month influence the light fixture sales.The manufacturer randomly selects 10 months and collects the following data: $$\begin{array} { l l l l } 
\text { Sales } & \text { Advertising } & \text { Price } & \text { \# of stores } \
41 & 20 & 40 & 1 \
42 & 40 & 60 & 3 \
59 & 40 & 20 & 4 \
60 & 50 & 80 & 5 \
81 & 50 & 10 & 6 \
80 & 60 & 40 & 6 \
100 & 70 & 20 & 7 \
82 & 70 & 60 & 8 \
101 & 80 & 30 & 9 \
110 & 90 & 40 & 10
\end{array}$$ The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,the price is the unit retail price for the particular month.Using this data,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores $$\begin{array} { l l l l l } 
\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \
\text { Constant } & 30.992 & 7.728 & 4.01 & 0.007 \
\text { Advertising } & 0.8202 & 0.5023 & 1.63 & 0.154 \
\text { Price } & - 0.32502 & 0.08935 & - 3.64 & 0.011 \
\text { Stores } & 1.841 & 3.855 & 0.48 & 0.650
\end{array}$$ S = 5.465R-Sq = 96.7%R-Sq(adj)= 95.0%
Analysis of Variance $$\begin{array} { l l l l l l } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 3 & 5179.2 & 1726.4 & 57.81 & 0.000 \
\text { Residual Error } & 6 & 179.2 & 29.9 & & \
\text { Total } & 9 & 5358.4 & & &
\end{array}$$
-Interpret the regression coefficients for the variables advertising,price,and store.

Accepted Answer

For each additional hundred dollars of advertising,the average light fixture sales are estimated to increase by an average of 820 units,if the value of the independent variable is within the experimental region and the other two independent variables are held constant.For each additional dollar of increase in the price of the fixture,the average number of fixtures sold is estimated to decrease by an average 330 units,if the value of the independent variable is within the experimental region and the other two independent variables are held constant.For each additional retail store used to sell the light fixture,the average sales are estimated to increase by an average of 1840 units,if the value of the independent variable is within the experimental region and the other two independent variables are held constant.

Question 3

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below:
$\begin{array} { l c l } \text { Predictor } & \text { Coef } & \text { SE Coef } \ \text { Constant } & 35.178 & 7.595 \ \text { Degree } & 0.22073 & 0.07131 \ \text { Age } & 0.3353 & 0.1901 \ \text { Salary } & 0.0930 & 0.1675 \end{array}$
$s = 7.62090$
Analysis of Variance
$\begin{array} { l c c } \text { Source } & \text { DF } & \text { SS } \ \text { Regression } & 3 & 1053.09 \ \text { Residual Error } & 32 & 1858.50\\ \text { Source } & \text { DF } & \text { Seq SS } \ \text { Degree } & 1 & 672.10 \ \text { Age } & 1 & 363.09 \ \text { Salary } & 1 & 17.90 \end{array}$ 
-Using the results above,what is the mean square error?

Accepted Answer

A) 32.00 
B) 58.08 
C) 372.10 
D) 1858.50 
E) 17.90 
A) 32.00 
B) 58.08 
C) 372.10 
D) 1858.50 
E) 17.90 B

Question 4

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 total degrees of freedom?

Accepted Answer

A) 1 
B) 3 
C) 5 
D) 8 
E) 11 
A) 1 
B) 3 
C) 5 
D) 8 
E) 11

Question 5

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 $$\begin{array} { l c c } 
\text { Source } & \text { DF } & \text { SS } \
\text { Regression } & 3 & 1053.09 \
\text { Residual Error } & 32 & 1858.50
\end{array}$$ $$\begin{array} { l c c } 
\text { Source } & \text { DF } & \text { Seq SS } \
\text { Math Dgr } & 1 & 672.10 \
\text { Age } & 1 & 363.09 \
\text { Salary } & 1 & 17.90
\end{array}$$
-Test the overall usefulness of the model at ? = .01.Calculate F and make your decision.

Accepted Answer

F = 6.04,reject H₀ MSR = 1053.0

Question 6

A fitted multiple regression model yields an R2 of 0.64.Interpret this value.

Accepted Answer

A) 64% of the independent variables used in the regression model are highly correlated and may falsely suggest a curvilinear relationship exists between x and y when the true relationship is linear. 
B) 64% of the variation in the observed value of the dependent variable is explained by the regression model. 
C) The correlation between each pair of independent variables is 0.8 or -0.8. 
D) The fitted model predicts the dependent variable accurately 64% of the time. 
E) 64% of the independent variables in the model are capable of accurately predicting the dependent variable. 
A) 64% of the independent variables used in the regression model are highly correlated and may falsely suggest a curvilinear relationship exists between x and y when the true relationship is linear. 
B) 64% of the variation in the observed value of the dependent variable is explained by the regression model. 
C) The correlation between each pair of independent variables is 0.8 or -0.8. 
D) The fitted model predicts the dependent variable accurately 64% of the time. 
E) 64% of the independent variables in the model are capable of accurately predicting the dependent variable.

Question 7

In a multiple regression analysis,if the normal probability plot exhibits approximately a straight line,then it can be concluded that we have not significantly violated the assumption that,for any point in the experimental region,the population of potential error terms is normally distributed.

Accepted Answer

A) True 
 B)False

Question 8

When the quadratic regression model y = $\beta$ 
0+ $\beta$ 
1x + $\beta$ 
2x2+ ? is used,the term $\beta$ 
1 shows the rate of curvature of the parabola.

Accepted Answer

A) True 
 B)False

Question 9

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 $$\begin{array} { l c c } 
\text { Source } & \text { DF } & \text { SS } \
\text { Regression } & 3 & 1053.09 \
\text { Residual Error } & 32 & 1858.50
\end{array}$$ $$\begin{array} { l c c } 
\text { Source } & \text { DF } & \text { Seq SS } \
\text { Math Dgr } & 1 & 672.10 \
\text { Age } & 1 & 363.09 \
\text { Salary } & 1 & 17.90
\end{array}$$
-Calculate R2.

Accepted Answer

0.3617 R² =

Question 10

Below is a partial multiple regression ANOVA table.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 0.242 & 2 \
\text { Error } & 0.105 & 3
\end{array}$$
-What is the number of observations in the sample?

Accepted Answer

A) 2 
B) 10 
C) 6 
D) 18 
E) 12 
A) 2 
B) 10 
C) 6 
D) 18 
E) 12

Question 11

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R2.

Accepted Answer

A) always 
B) sometimes 
C) never 
A) always 
B) sometimes 
C) never

Question 12

A particular multiple regression model has 3 independent variables,the sum of the squared residuals is 7680,and the total number of observations is 34.Compute a point estimate for the standard error?

Accepted Answer

A) 256 
B) 232.72 
C) 225.89 
D) 16 
E) 15.03 
A) 256 
B) 232.72 
C) 225.89 
D) 16 
E) 15.03

Question 13

In the quadratic regression model y = ?0+ ?1x + ?2x2+ ?,if the term ?2is greater than zero,then the parabola opens __________.

Accepted Answer

Question 14

Regression models that employ more than one independent variable are referred to as multiple regression models.

Accepted Answer

A) True 
 B)False

Question 15

Consider the following partial computer output for a multiple regression model. $$\begin{array} { l l l } 
\text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \
\text { Constant } & 99.3883 & \
\text { X1 } & - 0.007207 & 0.0031 \
\text { X2 } & 0.0011336 & 0.00122 \
\text { X3 } & 0.9324 & 0.373 \
& & \
\text { Analysis of Variance } & & \text { SS } \
\text { Source } & \text { df } & 31.308 \
\text { Regression } & 3 & 9.378
\end{array}$$
-What is the total sum of squares,explained variation,and mean square error?

Accepted Answer

40.686,31.308,.5861

Question 16

Determine the 90% interval for β2 and interpret its meaning

Accepted Answer

(0.0135,0.6571)We are 90% confident that

Question 17

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 $$\begin{array} { l c c } 
\text { Source } & \text { DF } & \text { SS } \
\text { Regression } & 3 & 1053.09 \
\text { Residual Error } & 32 & 1858.50
\end{array}$$ $$\begin{array} { l c c } 
\text { Source } & \text { DF } & \text { Seq SS } \
\text { Math Dgr } & 1 & 672.10 \
\text { Age } & 1 & 363.09 \
\text { Salary } & 1 & 17.90
\end{array}$$
-Write the least squares prediction equation.

Accepted Answer

? = 35.178

Question 18

Below is a partial multiple regression computer output.
$$\begin{array} { l l l } 
\text { Source } & \text { SS } & \text { df } \
\text { Model } & 32,774 & 5 \
\text { Error } & 21,886 & 292 \
\text { Total } & 54,660 & 297
\end{array}$$
-What is number of observations in the sample?

Accepted Answer

A) 292 
B) 294 
C) 296 
D) 298 
E) 300 
A) 292 
B) 294 
C) 296 
D) 298 
E) 300

Question 19

Test the usefulness of variable "price" in the model using the null hypothesis H0: β2≤ 0,at alpha = 0.05,and state your conclusions.

Accepted Answer

Reject H₀.We have strong eviden

Question 20

Consider the following partial computer output for a multiple regression model.
$$\begin{array}{l}
\begin{array} { l l l } 
\text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \
\text { Constant } & 99.3883 & \
\mathrm { X } 1 & - 0.007207 & 0.0031 \
\mathrm { X } 2 & 0.0011336 & 0.00122 \
\mathrm { X } 3 & 0.9324 & 0.373
\end{array}\
\text { Analysis of Variance }\
\begin{array} { l l l } 
\text { Source } & \text { df } & \text { SS } \
\text { Regression } & 3 & 31.308 \
\text { Error (residual) } & 16 & 9.378
\end{array}
\end{array}$$
-What is the adjusted R2?

Accepted Answer

A) 31.308% 
B) 76.95% 
C) 87.72% 
D) 72.63% 
E) 23.1% 
A) 31.308% 
B) 76.95% 
C) 87.72% 
D) 72.63% 
E) 23.1%

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of _____ variables.

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 total degrees of freedom?

A fitted multiple regression model yields an R² of 0.64.Interpret this value.

In a multiple regression analysis,if the normal probability plot exhibits approximately a straight line,then it can be concluded that we have not significantly violated the assumption that,for any point in the experimental region,the population of potential error terms is normally distributed.

When the quadratic regression model y = $\beta$ 0+ $\beta$ 1x + $\beta$ 2x²+ ? is used,the term $\beta$ 1 shows the rate of curvature of the parabola.

Below is a partial multiple regression ANOVA table. Source SS df Model 0.242 2 Error 0.105 3 -What is the number of observations in the sample?

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

A particular multiple regression model has 3 independent variables,the sum of the squared residuals is 7680,and the total number of observations is 34.Compute a point estimate for the standard error?

In the quadratic regression model y = ?₀+ ?₁x + ?₂x²+ ?,if the term ?₂is greater than zero,then the parabola opens __________.

Regression models that employ more than one independent variable are referred to as multiple regression models.

Determine the 90% interval for β₂ and interpret its meaning

Below is a partial multiple regression computer output. Source SS df Model 32,774 5 Error 21,886 292 Total 54,660 297 -What is number of observations in the sample?

Test the usefulness of variable "price" in the model using the null hypothesis H₀: β₂≤ 0,at alpha = 0.05,and state your conclusions.

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 df SS Regression 3 31.308 Error (residual) 16 9.378 -What is the adjusted R²?

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

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of _____ variables.

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 total degrees of freedom?

A fitted multiple regression model yields an R2 of 0.64.Interpret this value.

In a multiple regression analysis,if the normal probability plot exhibits approximately a straight line,then it can be concluded that we have not significantly violated the assumption that,for any point in the experimental region,the population of potential error terms is normally distributed.

When the quadratic regression model y = β\betaβ 0+ β\betaβ 1x + β\betaβ 2x2+ ? is used,the term β\betaβ 1 shows the rate of curvature of the parabola.

Below is a partial multiple regression ANOVA table. Source SS df Model 0.242 2 Error 0.105 3 -What is the number of observations in the sample?

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R2.

A particular multiple regression model has 3 independent variables,the sum of the squared residuals is 7680,and the total number of observations is 34.Compute a point estimate for the standard error?

In the quadratic regression model y = ?0+ ?1x + ?2x2+ ?,if the term ?2is greater than zero,then the parabola opens __________.

Regression models that employ more than one independent variable are referred to as multiple regression models.

Determine the 90% interval for β2 and interpret its meaning

Below is a partial multiple regression computer output. Source SS df Model 32,774 5 Error 21,886 292 Total 54,660 297 -What is number of observations in the sample?

Test the usefulness of variable "price" in the model using the null hypothesis H0: β2≤ 0,at alpha = 0.05,and state your conclusions.

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 df SS Regression 3 31.308 Error (residual) 16 9.378 -What is the adjusted R2?

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

A fitted multiple regression model yields an R² of 0.64.Interpret this value.

When the quadratic regression model y = $\beta$ 0+ $\beta$ 1x + $\beta$ 2x²+ ? is used,the term $\beta$ 1 shows the rate of curvature of the parabola.

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

In the quadratic regression model y = ?₀+ ?₁x + ?₂x²+ ?,if the term ?₂is greater than zero,then the parabola opens __________.

Determine the 90% interval for β₂ and interpret its meaning

Test the usefulness of variable "price" in the model using the null hypothesis H₀: β₂≤ 0,at alpha = 0.05,and state your conclusions.

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 df SS Regression 3 31.308 Error (residual) 16 9.378 -What is the adjusted R²?