Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. \[\begin{array}{l} \begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\ 12.924 & 4.425 \\ - 3.682 & 2.630 \\ 45.216 & 12.560 \end{array}\\ \text { Analysis of Variance }\\ \begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\ \text { Variation } & \text { Freedom } & \text { Squares } & \text { Square } \end{array} \quad F \end{array}\] The interpretation of the coefficient of x1 is that

A) a one unit change in x1 will lead to a 3.682 unit decrease in y. B) a one unit increase in x1 will lead to a 3.682 unit decrease in y when all other variables are held constant. C) a one unit increase in x1 will lead to a 3.682 unit decrease in x2 when all other variables are held constant. D) The unit of measurement for y is required to interpret the coefficient. A) a one unit change in x1 will lead to a 3.682 unit decrease in y. B) a one unit increase in x1 will lead to a 3.682 unit decrease in y when all other variables are held constant. C) a one unit increase in x1 will lead to a 3.682 unit decrease in x2 when all other variables are held constant. D) The unit of measurement for y is required to interpret the coefficient.

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). $\hat { y }$ = 30 + .7x1 + 3x2 Also provided are SST = 1200 and SSE = 384.If we want to test for the significance of the model, the critical value of F at $\alpha$ = .05 is

A) 3.33. B) 3.35. C) 3.34. D) 2.96. A) 3.33. B) 3.35. C) 3.34. D) 2.96.

Below you are given a partial multiple regression computer output based on a sample of 30 days of the price of a company's stock (y in dollars), the Dow Jones Industrial Average (x1), and the stock price of the company's major competitor (x2 in dollars). $\begin{array}{lll} & \text { Coefficients } & \text { Standard Error } \\ \text { Constant } & 20.000 & 5.455 \\ \mathrm{x}_{1} & 0.006 & 0.002 \\ \mathrm{x}_{2} & -0.70 & 0.200 \end{array}$ a. Use the output shown above and write an equation that can be used to predict the price of the stock. b. If the Dow Jones Industrial Average is 10,000 and the price of the major competitor is $50, what would you expect the price of the stock to be? c. At α = .05, test to determine if the Dow Jones average is a significant variable. d. At α = .05, test to determine if the stock price of the major competitor is a significant variable.

a. @#IMG-DLM& = 20 + .006x 1 - .7x 2 b. $4

The Brock Juice Company has developed a regression model relating sales (y in $10,000s) with four independent variables.The four independent variables are price per unit (x1, in dollars), competitor's price (x2, in dollars), advertising (x3, in $1000s), and type of container used (x4) (1 = Cans and 0 = Bottles).Part of the regression results is shown below: ANOVA $\begin{array}{lll} \text { Source } & d f & S S \\ \text { Regression } & 4 & 283,940.60 \\ \text { Error (Residuals) } & 18 & 621,735.14 \end{array}$ a. Compute the multiple coefficient of determination and fully interpret its meaning. b. Is the regression model significant? Explain what your answer implies. Let α = .05. c. What has been the sample size for this analysis?

a. .3135; 31.35% of the variation in s

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. \[\begin{array}{l} \begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\ 12.924 & 4.425 \\ - 3.682 & 2.630 \\ 45.216 & 12.560 \end{array}\\ \text { Analysis of Variance }\\ \begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\ \text { Variation } & \text { Freedom } & \text { Squares } & \text { Square } \end{array} \quad F \end{array}\] The t value obtained from the table which is used to test an individual parameter at the 1% level is

A) 2.650. B) 2.921. C) 2.977. D) 3.012. A) 2.650. B) 2.921. C) 2.977. D) 3.012.

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: $\hat { y }$ = 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18.The coefficient of the unit price indicates that if the unit price is

A) increased by $1 (holding advertisement constant), sales are expected to increase by $3. B) decreased by $1 (holding advertisement constant), sales are expected to decrease by $3. C) increased by $1 (holding advertisement constant), sales are expected to increase by $4000. D) increased by $1 (holding advertisement constant), sales are expected to decrease by $3000. A) increased by $1 (holding advertisement constant), sales are expected to increase by $3. B) decreased by $1 (holding advertisement constant), sales are expected to decrease by $3. C) increased by $1 (holding advertisement constant), sales are expected to increase by $4000. D) increased by $1 (holding advertisement constant), sales are expected to decrease by $3000.

Exam 15: Multiple Regression

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error 12.924 4.425 -3.682 2.630 45.216 12.560 Analysis of Variance Source of Degrees of Sum of Mean Variation Freedom Squares Square F The interpretation of the coefficient of x₁ is that

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Question 21

For a multiple regression model, SST = 200 and SSE = 50.The multiple coefficient of determination is

(Multiple Choice)

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Question 22

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). $\hat { y }$ = 30 + .7x₁ + 3x₂ Also provided are SST = 1200 and SSE = 384.If we want to test for the significance of the model, the critical value of F at $\alpha$ = .05 is

(Multiple Choice)

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Question 23

A regression model involved 18 independent variables and 200 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

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Question 24

If an independent variable is added to a multiple regression model, the R² value

(Multiple Choice)

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Question 25

For a multiple regression model, SSR = 600 and SSE = 200.The multiple coefficient of determination is

(Multiple Choice)

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Question 26

The _______ of an observation is determined by how far the values of the independent variables are from their means.

(Multiple Choice)

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Question 27

A regression analysis involved 8 independent variables and 99 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

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Question 28

A regression analysis was applied to determine the relationship between a dependent variable and 4 independent variables and the following information was obtained. R Square = .80 SSR = 680 Total number of observations, n = 45 a. Fill in all the blanks in the following ANOVA table. b. At α = .05, test to determine if the model is significant. ANOVA df SS MS F Regression \_\_\_? \_\_\_? \_\_\_? \_\_\_? Error (residual) \_\_\_? \_\_\_? \_\_\_? Total \_\_\_? \_\_\_?

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Question 29

In a regression analysis involving 18 observations and four independent variables, the following information was obtained. Multiple R $= .6000$ R Square $= .3600$ Standard Error $= 4.8000$ Based on the above information, fill in all the blanks in the following ANOVA table. ANOVA df SS MS F Regression \_\_\_? \_\_\_? \_\_\_? \_\_\_? Error \_\_\_? \_\_\_? \_\_\_?

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Question 30

Below you are given a partial multiple regression computer output based on a sample of 30 days of the price of a company's stock (y in dollars), the Dow Jones Industrial Average (x₁), and the stock price of the company's major competitor (x₂ in dollars). Coefficients Standard Error Constant 20.000 5.455 0.006 0.002 -0.70 0.200 a. Use the output shown above and write an equation that can be used to predict the price of the stock. b. If the Dow Jones Industrial Average is 10,000 and the price of the major competitor is $50, what would you expect the price of the stock to be? c. At α = .05, test to determine if the Dow Jones average is a significant variable. d. At α = .05, test to determine if the stock price of the major competitor is a significant variable.

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Question 31

A regression was performed on a sample of 20 observations.Two independent variables were included in the analysis, x and z.The relationship between x and z is z = x².The following estimated equation was obtained. $\hat { y }$ = 23.72 + 12.61x + .798z The standard errors for the coefficients are sb₁ = 4.85 and sb₂ = .21.For this model, SSR = 520.2 and SSE = 340.6. a. Estimate the value of y when x = 5. b. Compute the appropriate t ratios. c. Test for the significance of the coefficients at the 5% level. Which variable(s) is(are) significant? d. Compute the multiple coefficient of determination and the adjusted multiple coefficient of determination. Interpret the meaning of the multiple coefficient of determination. e. Test the significance of the relationship among the variables at the 5% level of significance.

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Question 32

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

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Question 33

The Brock Juice Company has developed a regression model relating sales (y in $10,000s) with four independent variables.The four independent variables are price per unit (x₁, in dollars), competitor's price (x₂, in dollars), advertising (x₃, in $1000s), and type of container used (x₄) (1 = Cans and 0 = Bottles).Part of the regression results is shown below: ANOVA Source df SS Regression 4 283,940.60 Error (Residuals) 18 621,735.14 a. Compute the multiple coefficient of determination and fully interpret its meaning. b. Is the regression model significant? Explain what your answer implies. Let α = .05. c. What has been the sample size for this analysis?

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Question 34

Below you are given a partial computer output relating the price of a company's stock (y in dollars), the Dow Jones Industrial Average (x₁), and the stock price of the company's major competitor (x₂ in dollars). ANOVA df SS MS F Regression Residual 20 40 Total 800 a. What has been the sample size for this regression analysis? b. At α = .05, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable. c. Determine the multiple coefficient of determination.

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Question 35

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error 12.924 4.425 -3.682 2.630 45.216 12.560 Analysis of Variance Source of Degrees of Sum of Mean Variation Freedom Squares Square F The t value obtained from the table which is used to test an individual parameter at the 1% level is

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Question 36

In a multiple regression model, the variance of the error term ε is assumed to be

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Question 37

A regression model between sales (y in $1000), unit price (x₁ in dollars), and television advertisement (x₂ in dollars) resulted in the following function: $\hat { y }$ = 7 - 3x₁ + 5x₂ For this model, SSR = 3500, SSE = 1500, and the sample size is 18.The coefficient of the unit price indicates that if the unit price is

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Question 38

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

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Question 39

A regression model relating units sold (y), price (x₁), and whether or not promotion for sales was used (x₂ = 1 if promotion was used and 0 if not) resulted in the following estimated equation. $\hat { y }$ = 120 - .03x₁ + .7x₂ and the following information is also provided. $n = 15 \quad s b _ { 1 } = .01 \quad s b _ { 2 } = .10$ a. Is price a significant variable? Let α = .05. b. Is promotion significant? Let α = .05.

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Question 40

For a multiple regression model, SST = 200 and SSE = 50.The multiple coefficient of determination is

A regression model involved 18 independent variables and 200 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

If an independent variable is added to a multiple regression model, the R² value

For a multiple regression model, SSR = 600 and SSE = 200.The multiple coefficient of determination is

The _______ of an observation is determined by how far the values of the independent variables are from their means.

A regression analysis involved 8 independent variables and 99 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

In a multiple regression model, the variance of the error term ε is assumed to be

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

Data and Statistics

Descriptive Statistics: Tabulargraphical

Descriptive Statistics: Numerical

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

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Filters

Exam 15: Multiple Regression

For a multiple regression model, SST = 200 and SSE = 50.The multiple coefficient of determination is

A regression model involved 18 independent variables and 200 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

If an independent variable is added to a multiple regression model, the R2 value​

For a multiple regression model, SSR = 600 and SSE = 200.The multiple coefficient of determination is

The _______ of an observation is determined by how far the values of the independent variables are from their means.​

A regression analysis involved 8 independent variables and 99 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

In a multiple regression model, the variance of the error term ε is assumed to be

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

Data and Statistics

Descriptive Statistics: Tabulargraphical

Descriptive Statistics: Numerical

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

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Filters

If an independent variable is added to a multiple regression model, the R² value

The _______ of an observation is determined by how far the values of the independent variables are from their means.