Deck 15: Multiple Regression

Question 1

The numerical value of the coefficient of determination.

A) is always larger than the coefficient of correlation.
B) is always smaller than the coefficient of correlation.
C) is negative if the coefficient of correlation is negative.
D) can be larger or smaller than the coefficient of correlation.

Answer 1

can be larger or smaller than the coefficient of correlation.

Question 2

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

A) zero.
B) -1.
C) 1.
D) any value.

Answer 2

zero.

Question 3

A regression model in which more than one independent variable is used to predict the dependent variable is called

A) a simple linear regression model.
B) a multiple regression model.
C) an independent model.
D) an adjusted prediction model.

Answer 3

a multiple regression model.

Question 4

In multiple regression analysis, the correlation among the independent variables is termed

A) adjusted correlation.
B) linearity.
C) multicollinearity.
D) adjusted coefficient of determination.

Question 5

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

A) 47 and 3.
B) 3 and 47.
C) 2 and 43.
D) 3 and 43.

Question 6

In multiple regression analysis,

A) there can be any number of dependent variables, but only one independent variable.
B) the adjusted coefficient of determination can never be negative.
C) the multiple coefficient of determination must be larger than 1.
D) there can be several independent variables, but only one dependent variable.

Question 7

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical independent variables in a regression model is called

A) an interaction.
B) a constant variable.
C) a dummy variable.
D) a logit variable.

Question 8

A measure of identifying the effect of an unusual x value on the regression results is called

A) Cook's D.
B) Leverage.
C) odd ratio.
D) unusual regression.

Question 9

In regression analysis, the response variable is the

A) independent variable.
B) dependent variable.
C) slope of the regression function.
D) intercept.

Question 10

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

A) the same for all values of the dependent variable.
B) zero.
C) the same for all values of the independent variable.
D) one.

Question 11

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.

Question 12

A term used to describe the case when the independent variables in a multiple regression model are correlated is

A) regression.
B) correlation.
C) multicollinearity.
D) leverage.

Question 13

The equation which has the form of E(y) = $\hat { y }$ = b₀ + b₁x₁ + b₂x₂ + ...+ b_px_p is

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

Question 14

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

Question 15

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

A) zero.
B) dependent on each other.
C) independent of each other.
D) always negative.

Question 16

The adjusted multiple coefficient of determination is adjusted for the

A) number of dependent variables.
B) number of independent variables.
C) number of equations.
D) sample size.

Question 17

The mathematical equation which has the form of E(y) = β₀ + β₁x₁ + β₂x₂ + ...+ β_pxp relating the expected value of the dependent variable to the value of the independent variables is

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

Question 18

A measure of goodness of fit for the estimated regression equation is the

A) multiple coefficient of determination.
B) multicollinearity.
C) mean square due to regression.
D) studentized residual.

Question 19

A multiple regression model has

A) only one independent variable.
B) more than one dependent variable.
C) more than one independent variable.
D) at least two dependent variables.

Question 20

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.

Question 21

A multiple regression model has the estimated form $\hat { y }$ = 5 + 6x + 7w

As x increases by 1 unit (holding w constant), y is expected to

A) increase by 11 units.
B) decrease by 11 units.
C) increase by 6 units.
D) decrease by 6 units.

Question 22

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

A) .25.
B) .33.
C) .80.
D) .75.

Question 23

A regression model involved 5 independent variables and 136 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

A) 121 degrees of freedom.
B) 135 degrees of freedom.
C) 130 degrees of freedom.
D) 4 degrees of freedom.

Question 24

In multiple regression analysis, a variable that cannot be measured in numerical terms is called a

A) nonmeasurable random variable.
B) constant variable.
C) dependent variable.
D) categorical independent variable.

Question 25

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

A) 18 degrees of freedom.
B) 200 degrees of freedom.
C) 199 degrees of freedom.
D) 181 degrees of freedom.

Question 26

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

A) SSR = SST + SSE.
B) SSR = SST - SSE.
C) SSE = SSR + SST.
D) n(SST) = p(SSR) + (n - p)(SSE).

Question 27

The multiple coefficient of determination is

A) MSR/MST.
B) MSR/MSE.
C) SSR/SST.
D) SSE/SSR.

Question 28

A multiple regression model has the estimated form $\hat { y }$ = 7 + 2x₁ + 9x₂

As x₁ increases by 1 unit (holding x₂ constant), y is expected to

A) increase by 9 units.
B) decrease by 9 units.
C) increase by 2 units.
D) decrease by 2 units.

Question 29

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?

A) t test
B) F test
C) Either a t test or a chi-square test can be used.
D) chi-square test

Question 30

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

A) 14 and 255.
B) 255 and 14.
C) 13 and 240.
D) 14 and 240.

Question 31

In a situation where the dependent variable can assume only one of the two possible discrete values,

A) we must use multiple regression.
B) there can only be two independent variables.
C) logistic regression should be applied.
D) all the independent variables must have values of either zero or one.

Question 32

The ratio of MSR to MSE yields

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

Question 33

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

A) .333.
B) .275.
C) .30.
D) .75.

Question 34

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240.The multiple coefficient of determination is

A) .300.
B) .192.
C) .500.
D) .700.

Question 35

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42.The multiple coefficient of determination is

A) .81.
B) .11.
C) .35.
D) .65.

Question 36

In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A) 8 and 121.
B) 7 and 120.
C) 8 and 112.
D) 7 and 112.

Question 37

In logistic regression,

A) there can only be two independent variables.
B) there are two dependent variables.
C) the dependent variable only assumes two discrete values.
D) the dependent variable only assumes two continuous values.

Question 38

In a multiple regression analysis, SSR = 1000 and SSE = 200.The F statistic for this model is

A) 5.
B) 1200.
C) 800.
D) Not enough information is provided to answer this question.

Question 39

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

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

Question 40

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

A) 98 degrees of freedom.
B) 97 degrees of freedom.
C) 90 degrees of freedom.
D) 7 degrees of freedom.

Question 41

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.

Question 42

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.To test for the significance of the model, the test statistic F is

A) 2.33.
B) .70.
C) 17.5.
D) 1.75.

Question 43

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄

For this model, SSR = 700 and SSE = 100.The computed F statistic for testing the significance of the above model is

A) 43.75.
B) 4.00.
C) 50.19.
D) 7.00.

Question 44

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 x₂ indicates that if television advertisement is increased by $1 (holding the unit price constant), sales are expected to

A) increase by $5.
B) increase by $12,000.
C) increase by $5000.
D) decrease by $2000.

Question 45

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄

For this model, SSR = 700 and SSE = 100.At the 5% level,

A) there is no evidence that the model is significant.
B) it can be concluded that the model is significant.
C) the conclusion is that the slope of x₁ is significant.
D) there is evidence that the slope of x₂ is significant.

Question 46

A regression analysis involved 6 independent variables and 27 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

A) 27 degrees of freedom.
B) 26 degrees of freedom.
C) 21 degrees of freedom.
D) 20 degrees of freedom.

Question 47

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄

For this model, SSR = 700 and SSE = 100.The critical F value at $\alpha$ = .05 is

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

Question 48

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $$\begin{array}{l}\begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\12.924 & 4.425 \\- 3.682 & 2.630 \\45.216 & 12.560\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }\end{array} \quad F\end{array}$$
Carry out the test of significance for the parameter $\beta$ ₁ at the 1% level.The null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised to test using F statistic.
D) be tested for ?_? instead.

Question 49

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.
$\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃

For this model, SSR = 600 and SSE = 400.MSR for this model is

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

Question 50

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 degrees of freedom for the sum of squares explained by the regression (SSR) are

A) 2.
B) 3.
C) 13.
D) 15.

Question 51

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃

For this model, SSR = 600 and SSE = 400.The multiple coefficient of determination for the above model is

A) .667.
B) .600.
C) .336.
D) .400.

Question 52

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.

Question 53

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $$\begin{array}{l}\begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\12.924 & 4.425 \\- 3.682 & 2.630 \\45.216 & 12.560\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }\end{array} \quad F\end{array}$$
We want to test whether the parameter $\beta$ ₁ is significant.The test statistic equals

A) -1.4.
B) 1.4.
C) 3.6.
D) -5.0.

Question 54

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.
$\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃

For this model, SSR = 600 and SSE = 400.The computed F statistic for testing the significance of the above model is

A) 1.50.
B) 20.00.
C) .600.
D) .667.

Question 55

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.

Question 56

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 adjusted multiple coefficient of determination for this problem is

A) .70.
B) .8367.
C) .66.
D) .2289.

Question 57

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.To test for the significance of the model, the p-value is

A) less than .01.
B) between .01 and .025.
C) between .025 and .05.
D) greater than .10.

Question 58

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A) 4 and 36.
B) 3 and 35.
C) 4 and 31.
D) 4 and 32.

Question 59

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40.The multiple coefficient of determination is

A) .80.
B) .90.
C) .25.
D) .15.

Question 60

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 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.

Question 61

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.The test statistic for testing the significance of the model is

A) .73.
B) 1.47.
C) 28.69.
D) 5.22.

Question 62

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.The multiple coefficient of determination is

A) .32.
B) .42.
C) .68.
D) .50.

Question 63

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

Question 64

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165
SSE = 60
​
The test statistic obtained from the information provided is

A) 2.110.
B) 3.480.
C) 5.455.
D) 6.875.

Question 65

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $$\begin{array}{l}\begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\12.924 & 4.425 \\- 3.682 & 2.630 \\45.216 & 12.560\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }\end{array} \quad F\end{array}$$
Carry out the test to determine if there is a relationship among the variables at the 5% level.The null hypothesis should

A) be rejected.
B) not be rejected.
C) be revised to test for multicollinearity.
D) test for individual significance instead.

Question 66

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165
SSE = 60
​
If we want to test for the significance of the model at a .05 level of significance, the critical F value (from the table) is

A) 3.06.
B) 3.48.
C) 3.34.
D) 3.11.

Question 67

As the value of the multiple coefficient of determination increases, ​

A) ​the value of the adjusted multiple coefficient of determination decreases.
B) ​the value of the regression equation's constant b₀ decreases.
C) ​the goodness of fit for the estimated multiple regression equation increases.
D) ​the value of the correlation coefficient decreases.

Question 68

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.The yearly income (in $) expected of a 24-year-old male individual is

A) $16,800.
B) $13,800.
C) $46,800.
D) $49,800.

Question 69

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.At the 5% level, the model

A) is significant.
B) is not significant.
C) would be significant if the sample size was larger than 30.
D) has significant individual parameters.

Question 70

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 F value obtained from the table which is used to test if there is a relationship among the variables at the 5% level equals

A) 3.41.
B) 3.63.
C) 3.81.
D) 19.41.

Question 71

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 test statistic used to determine if there is a relationship among the variables equals

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

Question 72

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.

Question 73

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.

Question 74

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.The estimated income (in $) of a 30-year-old male is

A) $51,000.
B) $21.
C) $90,000.
D) $51.

Question 75

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.The yearly income (in $) expected of a 24-year-old female individual is

A) $19.80.
B) $19,800.
C) $49.80.
D) $49,800.

Question 76

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 sum of squares due to error (SSE) equals

A) 373.31.
B) 485.3.
C) 4853.
D) 6308.9.

Question 77

Even though a residual may be unusually large, the standardized residual rule might fail to identify the observation as being an outlier.This difficulty can be circumvented by using​

A) categorical independent variables.
B) ​residual transformation.
C) ​studentized deleted residuals.
D) ​logistic regression.

Question 78

A regression analysis involved 17 independent variables and 697 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have​

A) ​696 degrees of freedom.
B) ​16 degrees of freedom.
C) 679 degrees of freedom.
D) ​714 degrees of freedom.

Question 79

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165
SSE = 60
​
The multiple coefficient of determination is

A) .3636.
B) .7333.
C) .275.
D) .5.

Question 80

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.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.