Question 1

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)None of the alternative answers are correct.

Accepted Answer

When the independent variables in a multiple regression model are correlated, it is known as multicollinearity. The presence of multicollinearity can result in unstable and unreliable estimates of the regression coefficients. Therefore, it is important to detect and address multicollinearity before interpreting the results of a multiple regression analysis.

Question 2

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

Accepted Answer

In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see a horizontal band of points centered near zero. This suggests that the residuals are randomly and evenly distributed around zero, indicating that the model is a good fit for the data and that the assumptions of linearity, independence, constant variance, and normality are met.  Option B is incorrect because a widening band of points suggests that the variability of the residuals is increasing as the predicted values increase, violating the constant variance assumption. Option C is incorrect because a band of points having a slope consistent with that of the regression equation suggests a pattern in the residuals, violating the assumption of randomness. Option D is incorrect because a parabolic band of points suggests a non-linear relationship between the predictor and response variables.

Question 3

In a multiple regression model, the error term$\varepsilon$is assumed to
A)have a mean of 1
B)have a variance of zero
C)have a standard deviation of 1
D)be normally distributed

Accepted Answer

The error term in a multiple regression model is assumed to be normally distributed with a mean of zero and a constant variance (i.e., homoscedasticity). Therefore, the best option is D, which states that the error term is normally distributed. A is incorrect because the error term has a mean of 0, not 1. B is incorrect because the error term must have a non-zero variance since it represents the variability in the dependent variable that is not explained by the independent variables. C is incorrect because the standard deviation of the error term is not necessarily 1, but rather it can vary depending on the data and model.

Question 4

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

Accepted Answer

The numerator degrees of freedom should be equal to the number of independent variables in the model, which is 14 in this case. The denominator degrees of freedom should be equal to the total sample size minus the number of independent variables, which is 255-14 = 241. However, since one degree of freedom is lost in estimating the intercept, the denominator degrees of freedom is actually 240. Therefore, the correct answer is D, with numerator degrees of freedom of 14 and denominator degrees of freedom of 240.

Question 5

In multiple regression analysis, the correlation among the independent variables is termed
A)homoscedasticity
B)linearity
C)multicollinearity
D)adjusted coefficient of determination

Accepted Answer

Multicollinearity refers to the correlation among the independent variables in a multiple regression analysis. If the independent variables are highly correlated, it can lead to instability in estimates of the regression coefficients and can make it difficult to interpret the individual effects of the independent variables on the dependent variable. Therefore, it is important to check for multicollinearity and address it if it is present in the data.

Question 6

In multiple regression analysis,
A)there can be any number of dependent variables but only one independent variable
B)there must be only one independent variable
C)the coefficient of determination must be larger than 1
D)there can be several independent variables, but only one dependent variable

Accepted Answer

In multiple regression analysis, there can be several independent variables, but only one dependent variable. Therefore, option D is correct. Options A and B are incorrect as they provide incorrect information about the number of dependent and independent variables. Option C is also incorrect as the coefficient of determination, R-squared, can only range from 0 to 1.

Question 7

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)None of these alternatives is correct.

Accepted Answer

A multiple regression model includes multiple independent variables to predict the dependent variable, whereas in a simple linear regression model, only one independent variable is used. An independent model is not a commonly used term in regression analysis.

Question 8

A multiple regression model has the form  = 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

Accepted Answer

According to the given model, the coefficient of x is 6, which means as x increases by 1 unit (holding w constant), y is expected to increase by 6 units. Therefore, the correct choice is C.

Question 9

In a multiple regression model, the values of the error term ,$\varepsilon$, are assumed to be
A)zero
B)dependent on each other
C)independent of each other
D)always negative

Accepted Answer

In a multiple regression model, the values of the error term are assumed to be independent of each other, meaning that the value of one error term does not affect the value of any other error term. This assumption is critical for the estimation of regression coefficients and the validity of hypothesis testing and confidence intervals.

Question 10

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

Accepted Answer

The answer of A regression model involved 18 independent variables...

Question 11

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

Accepted Answer

The numerator degrees of freedom will be equal to the number of independent variables in the model, which is 4. The denominator degrees of freedom will be equal to the total number of observations minus the number of independent variables, which is 36-4=32. Therefore, the critical value of F will be determined by the F-distribution with 4 and 32 degrees of freedom. Choice C is the only option that matches this.

Question 12

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

Accepted Answer

The numerator degrees of freedom is equal to the number of independent variables in the model, which is 8. The denominator degrees of freedom is equal to the total sample size minus the number of independent variables in the model minus 1, which is 121 - 8 - 1 = 112. Thus, the correct choice is C.

Question 13

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is
A)0.1389
B)0.1220
C)0.878
D)0.7317

Accepted Answer

The answer of In a multiple regression analysis involving 12...

Question 14

A variable that cannot be measured in numerical terms is called
A)a nonmeasurable random variable
B)a constant variable
C)a dependent variable
D)a qualitative variable

Accepted Answer

A qualitative variable is a variable that does not have numerical value or measurement, but rather a non-numerical characteristic such as color or type.

Question 15

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

Accepted Answer

The answer of A regression analysis involved 6 independent variables...

Question 16

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)713 degrees of freedom
D)714 degrees of freedom

Accepted Answer

The answer of A regression analysis involved 17 independent variables...

Question 17

The adjusted multiple coefficient of determination is adjusted for
A)the number of dependent variables
B)the number of independent variables
C)the number of equations
D)detrimental situations

Accepted Answer

The adjusted multiple coefficient of determination is adjusted for the number of independent variables. This is done to remove the effect of the number of independent variables on the coefficient of determination and to provide a more accurate measure of the goodness of fit of the regression model.

Question 18

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is
A)0.80
B)0.90
C)0.25
D)0.15

Accepted Answer

The formula for the coefficient of determination is:

R^2 = SSR / SST

where SSR is the sum of squares due to regression and SST is the total sum of squares. Since we know that SSR = 360, we need to find SST.

SST = SSR + SSE = 360 + 40 = 400

Now we can calculate R^2:

R^2 = SSR / SST = 360 / 400 = 0.90

Therefore, the answer is B (0.90). This means that 90% of the variation in the dependent variable can be explained by the independent variables in the model.

Question 19

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is
A)0.25
B)4.00
C)250
D)0.75

Accepted Answer

The multiple coefficient of determination is obtained by dividing the explained variation (SST - SSE) by the total variation (SST). Therefore, R-squared = (200-50)/200 = 0.75. The best choice is D.

Question 20

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is
A)0.81
B)0.11
C)0.35
D)0.65

Accepted Answer

The coefficient of determination is given by $R^2 = 1 - \frac{SSE}{SST}$. Plugging in the given values, we get $R^2 = 1 - \frac{42}{120} = 0.65$. Therefore, the answer is D.

Quiz 13: Multiple Regression

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

In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see

In a multiple regression model, the error term $\varepsilon$ is assumed to

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

In multiple regression analysis,

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

A multiple regression model has the form = 5 + 6x + 7w As x increases by 1 unit (holding w constant) , y is expected to

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

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

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

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

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

A variable that cannot be measured in numerical terms is called

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 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

The adjusted multiple coefficient of determination is adjusted for

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

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

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