Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18xS1U1B11S1U1B0 +43xS1U1B12S1U1B0 + 87xS1U1B13S1U1B0 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. MSR for this model is

A) 200 B) 10 C) 1,000 D) 43 A) 200 B) 10 C) 1,000 D) 43

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female). = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

A) is significant B) is not significant C) would be significant is the sample size was larger than 30 D) None of these alternatives is correct. A) is significant B) is not significant C) would be significant is the sample size was larger than 30 D) None of these alternatives is correct.

Exhibit 15-2 A regression model between sales (y in $1,000), unit price (xS1U1B11S1U1B0 in dollars) and television advertisement (xS1U1B12S1U1B0 in dollars) resulted in the following function: = 7 - 3xS1U1B11S1U1B0 + 5xS1U1B12S1U1B0 For this model SSR = 3500, SSE = 1500, and the sample size is 18. -Refer to Exhibit 15-2. If SSR = 600 and SSE = 300, the test statistic F is

A) 2.33 B) 0.70 C) 17.5 D) 1.75 A) 2.33 B) 0.70 C) 17.5 D) 1.75

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18xS1U1B11S1U1B0 +43xS1U1B12S1U1B0 + 87xS1U1B13S1U1B0 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. The coefficient of determination for the above model is

A) 0.667 B) 0.600 C) 0.336 D) 0.400 A) 0.667 B) 0.600 C) 0.336 D) 0.400

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4xS1U1B11S1U1B0 - 3xS1U1B12S1U1B0 + 8xS1U1B13S1U1B0 + 8xS1U1B14S1U1B0 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is

A) 2.53 B) 2.69 C) 2.76 D) 2.99 A) 2.53 B) 2.69 C) 2.76 D) 2.99

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female). = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0 Also provided are SST = 1,200 and SSE = 384. -In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see

A) a horizontal band of points centered near zero B) a widening band of points C) a band of points having a slope consistent with that of the regression equation D) a parabolic band of points A) a horizontal band of points centered near zero B) a widening band of points C) a band of points having a slope consistent with that of the regression equation D) a parabolic band of points

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female). = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0 Also provided are SST = 1,200 and SSE = 384. -The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, ..., xp and the error term $\varepsilon$ is

A) a simple nonlinear regression model B) a multiple regression model C) an estimated multiple regression equation D) a multiple regression equation A) a simple nonlinear regression model B) a multiple regression model C) an estimated multiple regression equation D) a multiple regression equation

Exam 15: Multiple Regression

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. MSR for this model is

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Question 41

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

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Question 42

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. $Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. We want to test whether the parameter \beta 1 is significant. The test statistic equals$ -Refer to Exhibit 15-5. We want to test whether the parameter $\beta$ ₁ is significant. The test statistic equals

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Question 43

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

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Question 44

The Natural Drink Company has developed a regression model relating its sales (y in $10,000s) with four independent variables. The four independent variables are price per unit (PRICE, in dollars), competitor's price (COMPRICE, in dollars), advertising (ADV, in $1,000s) and type of container used (CONTAIN; 1 = Cans and 0 = Bottles). Part of the regression results is shown below. (Assume n = 25) $The Natural Drink Company has developed a regression model relating its sales (y in $10,000s) with four independent variables. The four independent variables are price per unit (PRICE, in dollars), competitor's price (COMPRICE, in dollars), advertising (ADV, in $1,000s) and type of container used (CONTAIN; 1 = Cans and 0 = Bottles). Part of the regression results is shown below. (Assume n = 25) a.If the manufacturer uses can containers, his price is $1.25, advertising $200,000, and his competitor's price is $1.50, what is your estimate of his sales? Give your answer in dollars. b.Test to see if there is a significant relationship between sales and unit price. Let \alpha = 0.05. c.Test to see if there is a significant relationship between sales and advertising. Let \alpha = 0.05. d.Is the type of container a significant variable? Let \alpha = 0.05. e.Test to see if there is a significant relationship between sales and competitor's price. Let \alpha = 0.05.$ a.If the manufacturer uses can containers, his price is $1.25, advertising $200,000, and his competitor's price is $1.50, what is your estimate of his sales? Give your answer in dollars. b.Test to see if there is a significant relationship between sales and unit price. Let $\alpha$ = 0.05. c.Test to see if there is a significant relationship between sales and advertising. Let $\alpha$ = 0.05. d.Is the type of container a significant variable? Let $\alpha$ = 0.05. e.Test to see if there is a significant relationship between sales and competitor's price. Let $\alpha$ = 0.05.

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Question 45

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is

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Question 46

A regression model involving 3 independent variables for a sample of 20 periods resulted in the following sum of squares. $A regression model involving 3 independent variables for a sample of 20 periods resulted in the following sum of squares. a.Compute the coefficient of determination and fully explain its meaning. b.At \alpha = 0.05 level of significance, test to determine whether or not there is a significant relationship between the independent variables and the dependent variable.$ a.Compute the coefficient of determination and fully explain its meaning. b.At $\alpha$ = 0.05 level of significance, test to determine whether or not there is a significant relationship between the independent variables and the dependent variable.

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Question 47

Exhibit 15-2 A regression model between sales (y in $1,000), unit price (x₁ in dollars) and television advertisement (x₂ in dollars) resulted in the following function: = 7 - 3x₁ + 5x₂ For this model SSR = 3500, SSE = 1500, and the sample size is 18. -Refer to Exhibit 15-2. If SSR = 600 and SSE = 300, the test statistic F is

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Question 48

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. The coefficient of determination for the above model is

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Question 49

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares.SSE = 306 SST = 1800 a.Compute the coefficient of determination. b.At $\alpha$ = 0.05, test to determine whether or not the model is significant.

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Question 50

In a multiple regression model, the values of the error term , $\varepsilon$ , are assumed to be

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Question 51

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is

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Question 52

A multiple regression model has

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Question 53

Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age (x₁ in years), level of education (x₂ ranging from 1 to 5), and the person's gender (x₃ where 0 =female and 1=male). The following is a partial result of Excel output that was used on a sample of 20 individuals. $Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age (x1 in years), level of education (x2 ranging from 1 to 5), and the person's gender (x3 where 0 =female and 1=male). The following is a partial result of Excel output that was used on a sample of 20 individuals. a.Compute the coefficient of determination. b.Perform a t test and determine whether or not the coefficient of the variable level of education (i.e., x2) is significantly different from zero. Let \alpha = 0.05. c.At \alpha = 0.05, perform an F test and determine whether or not the regression model is significant. d.As you note the coefficient of x3 is -0.510. Fully interpret the meaning of this coefficient.$ a.Compute the coefficient of determination. b.Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., x₂) is significantly different from zero. Let $\alpha$ = 0.05. c.At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant. d.As you note the coefficient of x₃ is -0.510. Fully interpret the meaning of this coefficient.

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Question 54

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see

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Question 55

The prices of Rawlston, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of company's stocks sold (x₁), and the volume of exchange (in millions) on the New York Stock Exchange (x₂) are shown below. Excel was used to determine the least-squares regression equation. Part of the computer output is shown below. a.Use the output shown above and write an equation that can be used to predict the price of the stock. b.Interpret the coefficients of the estimated regression equation that you found in Part c.At 95% confidence, determine which variables are significant and which are not. d.If in a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be?

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Question 56

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). $Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). = 30 + 0.7x1 + 3x2 Also provided are SST = 1,200 and SSE = 384. -The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, ..., xp and the error term \varepsilon is$ = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -The mathematical equation that explains how the dependent variable y is related to several independent variables x₁, x₂, ..., x_p and the error term $\varepsilon$ is

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Question 57

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

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Question 58

The correct relationship between SST, SSR, and SSE is given by

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Question 59

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is

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Question 60

Showing 41 - 60 of 109

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. MSR for this model is

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. The coefficient of determination for the above model is

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares.SSE = 306 SST = 1800 a.Compute the coefficient of determination. b.At $\alpha$ = 0.05, test to determine whether or not the model is significant.

In a multiple regression model, the values of the error term , $\varepsilon$ , are assumed to be

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is

A multiple regression model has

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

The correct relationship between SST, SSR, and SSE is given by

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Exam 15: Multiple Regression

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x1 +43x2 + 87x3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. MSR for this model is

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). = 30 + 0.7x1 + 3x2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. We want to test whether the parameter β\betaβ 1 is significant. The test statistic equals

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x1 +43x2 + 87x3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. The coefficient of determination for the above model is

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares.SSE = 306 SST = 1800 a.Compute the coefficient of determination. b.At α\alphaα = 0.05, test to determine whether or not the model is significant.

In a multiple regression model, the values of the error term , ε\varepsilonε , are assumed to be

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x1 - 3x2 + 8x3 + 8x4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is

A multiple regression model has

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

The correct relationship between SST, SSR, and SSE is given by

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. MSR for this model is

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. The coefficient of determination for the above model is

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares.SSE = 306 SST = 1800 a.Compute the coefficient of determination. b.At $\alpha$ = 0.05, test to determine whether or not the model is significant.

In a multiple regression model, the values of the error term , $\varepsilon$ , are assumed to be

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is