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In a multiple regression analysis involving 10 independent variables and 165 observations, SSR = 878 and SSE = 122.The multiple coefficient of determination is


A) .1389.
B) .122.
C) .878.
D) .7317.

E) A) and B)
F) B) and C)

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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) . ​ The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x<sub>1</sub>) and their gender (x<sub>2</sub>) (0 if male and 1 if female) . ​ = 30 + .7x<sub>1</sub> + 3x<sub>2</sub> ​ Also provided are SST = 1200 and SSE = 384.From the above linear function for multiple regression, it can be said that the expected yearly income of A) males is $3 more than females. B) females is $3 more than males. C) males is $3000 more than females. D) females is $3000 more than males. = 30 + .7x1 + 3x2 ​ Also provided are SST = 1200 and SSE = 384.From the above linear function for multiple regression, it can be said that the expected yearly income of


A) males is $3 more than females.
B) females is $3 more than males.
C) males is $3000 more than females.
D) females is $3000 more than males.

E) None of the above
F) B) and D)

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A regression model between sales (y in $1000) , unit price (x1 in dollars) , and television advertisement (x2 in dollars) resulted in the following function: ​ A regression model between sales (y in $1000) , unit price (x<sub>1</sub> in dollars) , and television advertisement (x<sub>2</sub> in dollars) resulted in the following function: ​ = 8 - 4x<sub>1</sub> + 5x<sub>2</sub> ​ For this model, SSR = 3500, SSE = 1500, and the sample size is 20.To test for the significance of the model, the test statistic F is A) 19.83. B) 88.23. C) 17. D) 2.33. = 8 - 4x1 + 5x2 ​ For this model, SSR = 3500, SSE = 1500, and the sample size is 20.To test for the significance of the model, the test statistic F is


A) 19.83.
B) 88.23.
C) 17.
D) 2.33.

E) None of the above
F) A) and B)

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Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. ​ The test statistic used to determine if there is a relationship among the variables equals A) 1.40. B) .2. C) .77. D) 5. ​ The test statistic used to determine if there is a relationship among the variables equals


A) 1.40.
B) .2.
C) .77.
D) 5.

E) A) and D)
F) A) and C)

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The ratio of MSR to MSE yields


A) SST.
B) the F statistic.
C) SSR.
D) the chi-square statistic.

E) A) and D)
F) A) and B)

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Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. ​ The interpretation of the coefficient of x<sub>1</sub> is that A) a one unit change in x<sub>1</sub> will lead to a 7.682 unit decrease in y. B) a one unit increase in x<sub>1</sub> will lead to a 7.682 unit decrease in y when all other variables are held constant. C) a one unit increase in x<sub>1</sub> will lead to a 7.682 unit decrease in x<sub>2</sub> when all other variables are held constant. D) The unit of measurement for y is required to interpret the coefficient. ​ The interpretation of the coefficient of x1 is that


A) a one unit change in x1 will lead to a 7.682 unit decrease in y.
B) a one unit increase in x1 will lead to a 7.682 unit decrease in y when all other variables are held constant.
C) a one unit increase in x1 will lead to a 7.682 unit decrease in x2 when all other variables are held constant.
D) The unit of measurement for y is required to interpret the coefficient.

E) B) and D)
F) B) and C)

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In a multiple regression model involving 60 observations, the following estimated regression equation was obtained: In a multiple regression model involving 60 observations, the following estimated regression equation was obtained: = 30 + 18x<sub>1</sub> + 43x<sub>2</sub> + 87x<sub>3</sub>+ 90x<sub>4</sub> <sub> </sub> For this model, SSR = 800 and SST = 1400.MSR for this model is A) 200. B) 10. C) 1000. D) 43. = 30 + 18x1 + 43x2 + 87x3+ 90x4 For this model, SSR = 800 and SST = 1400.MSR for this model is


A) 200.
B) 10.
C) 1000.
D) 43.

E) A) and B)
F) B) and C)

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In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ = 20 + 5x<sub>1</sub> - 4x<sub>2</sub> + 8x<sub>3</sub> + 8x<sub>4</sub> ​ For this model, SSR = 700 and SSE = 100.The computed F statistic for testing the significance of the above model is A) 78.75. B) 82.25. C) 50.19. D) 7.00. = 20 + 5x1 - 4x2 + 8x3 + 8x4 ​ For this model, SSR = 700 and SSE = 100.The computed F statistic for testing the significance of the above model is


A) 78.75.
B) 82.25.
C) 50.19.
D) 7.00.

E) None of the above
F) B) and D)

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In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 380 and SSE = 45.The multiple coefficient of determination is


A) .80.
B) .89.
C) .25.
D) .11.

E) C) and D)
F) A) and B)

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


A) ​becomes larger or smaller depending on the statistical significance of the variable.
B) ​becomes larger even if the variable added is not statistically significant.
C) ​might or might not become larger even if the variable added is statistically significant.
D) is not affected by the variable added even if it is statistically significant.

E) B) and C)
F) A) and D)

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In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. ​ In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. ​ = 50+ 13x<sub>1</sub> + 40x<sub>2</sub> + 68x<sub>3</sub> ​ For this model, SSR = 600 and SSE = 300.MSR for this model is A) 200. B) 10. C) 1000. D) 43. = 50+ 13x1 + 40x2 + 68x3 ​ For this model, SSR = 600 and SSE = 300.MSR for this model is


A) 200.
B) 10.
C) 1000.
D) 43.

E) A) and D)
F) All of the above

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


A) ​odds ratio
B) ​residual
C) ​collinearity
D) ​leverage

E) A) and D)
F) B) and C)

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


A) have a mean of 1.
B) have a variance of zero.
C) have no distribution.
D) be normally distributed.

E) A) and B)
F) A) and C)

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Given the following data, find the least squares regression line that models the data. Given the following data, find the least squares regression line that models the data. ​ ​ ​ ​

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blured image = -9929.8...

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A regression analysis involved 8 independent variables and 100 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have


A) 9 degrees of freedom.
B) 97 degrees of freedom.
C) 91 degrees of freedom.
D) 7 degrees of freedom.

E) B) and C)
F) C) and D)

Correct Answer

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The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is a(n)


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

E) All of the above
F) A) and B)

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In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: ​ = 20 + 5x<sub>1</sub> - 4x<sub>2</sub> + 8x<sub>3</sub> + 8x<sub>4</sub> ​ For this model, SSR = 700 and SSE = 100.The multiple coefficient of determination for the above model is A) .934. B) .875. C) .125. D) .144. = 20 + 5x1 - 4x2 + 8x3 + 8x4 ​ For this model, SSR = 700 and SSE = 100.The multiple coefficient of determination for the above model is


A) .934.
B) .875.
C) .125.
D) .144.

E) C) and D)
F) A) and B)

Correct Answer

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In regression analysis, an outlier is an observation whose


A) mean is larger than the standard deviation.
B) residual is zero.
C) mean is zero.
D) residual is much larger than the rest of the residual values.

E) A) and B)
F) A) and C)

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In order to test for the significance of a regression model involving 14 independent variables and 260 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are


A) 14 and 260.
B) 260 and 14.
C) 13 and 245.
D) 14 and 245.

E) A) and B)
F) All of the above

Correct Answer

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A regression model involved 20 independent variables and 200 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have


A) 18 degrees of freedom.
B) 200 degrees of freedom.
C) 199 degrees of freedom.
D) 179 degrees of freedom.

E) A) and B)
F) B) and C)

Correct Answer

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