Question 1

A partial F test is used to assess when at least one variable in a subset of squared and interaction variables in the multiple regression model is significant.

Accepted Answer

This statement is true. A partial F test is a statistical test that assesses the significance of a subset of variables in a multiple regression model. It does this by comparing the model's full regression sum of squares (RSS) to a reduced RSS, which excludes the subset of variables. If the difference between these two RSS values is statistically significant, then at least one variable in the subset is considered to be significant.

Question 2

If it is desired to include marital status in a multiple regression model by using the categories single,married,separated,divorced,widowed,what will be the effect on the model?

Accepted Answer

In a multiple regression model, categorical variables like marital status are included using dummy variables. With five categories, four dummy variables are needed to represent them, as one category serves as the reference group.

Question 3

In multiple regression analysis,which one of the following is the appropriate notation for error (residual)?

Accepted Answer

The error or residual in multiple regression analysis is the difference between the actual value of the dependent variable and the predicted value (based on the independent variables). Therefore, the appropriate notation for error is the difference between the observed dependent variable (y) and the predicted value of y, represented by the fitted value (ŷ). This is option B: yᵢ - ŷᵢ. Option A represents the deviation of each observation from the mean, which is not the same as the residual, while options C and D represent the difference between two estimates, which is not a residual. Therefore, the correct answer is B.

Question 4

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

Accepted Answer

If these conditions exist, the model should be considered desirable.

Question 5

In multiple regression analysis,the mean square regression divided by mean square error yields the _________.

Accepted Answer

The mean square regression divided by mean square error yields the F statistic in multiple regression analysis, which assesses whether the regression model as a whole explains a significant proportion of variance in the dependent variable.

Question 6

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee salaries for the company in question.In this multiple regression model,the salaries are in thousands of dollars.For example,a data entry of 35 for the dependent variable indicates a salary of $35,000.The indicator (dummy)variable for gender is coded as X₁ = 0 if male and X₁ = 1 if female.The computer output of this multiple regression model shows that the coefficient for this variable (X₁)is -4.2.The t test showed that X₁ was significant at α = 0.1.This result implies that for male and female workers of the company,

Accepted Answer

The coefficient for the gender indicator variable (X₁) is -4.2, which means that being female (X₁ = 1) is associated with a $4200 lower salary compared to being male (X₁ = 0). This result is significant at α = 0.1, which means that the probability of observing such a large difference in salaries between males and females by chance is less than 10%. Therefore, the best choice is A: On the average, females earn $4200 less.

Question 7

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

Accepted Answer

The adjusted multiple coefficient of determination is always less than R² because it takes into account the number of independent variables in the model. The more independent variables in the model, the smaller the adjusted multiple coefficient of determination will be.

Question 8

The range of feasible values for the multiple coefficient of correlation is from ________.

Accepted Answer

The multiple coefficient of correlation ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation. Therefore, option C is the correct answer.

Question 9

The range of feasible values for the multiple coefficient of determination is from ________.

Accepted Answer

The coefficient of determination, denoted by R-squared, is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It takes a value between 0 and 1. When the value is closer to 1, it indicates that the regression model is better at predicting the outcome, and the dependent variable is more strongly related to the independent variable(s). Therefore, the possible range of feasible values is from 0 to 1.

Question 10

The mean square error of a multiple regression model with k independent variables and n observations is __________.

Accepted Answer

MSE = SSE / [n − (k + 1)]

Question 11

When using a multiple regression model,we assume that error terms (residuals)are distributed according to a(n)________________ distribution.

Accepted Answer

The assumption in multiple regression is that the error terms (residuals) are normally distributed with a mean of zero and constant variance. Therefore, option B - Normal distribution - is the best choice. The other distributions listed - Binomial, Exponential, and Poisson - are not appropriate for error term residuals in a multiple regression model.

Question 12

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

Accepted Answer

A high simple correlation coefficient between the dependent variable and one independent variable does not indicate multicollinearity, which involves high correlations among independent variables, not between an independent and the dependent variable.

Question 13

Even when encountering extreme multicollinearity with the use of squared and interaction variables,t tests on the significance of individual independent variables is reliable.

Accepted Answer

When extreme multicollinearity is present, t tests on the significance of individual independent variables can produce unreliable and erroneous results. This is because the coefficients for the correlated variables are difficult to estimate accurately and their significance tests may not reflect their true contribution to the model. In such cases, other techniques such as regularization or PCA may be more appropriate.

Question 14

The graph of the prediction equation obtained from the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$
Is a(n)__________.

Accepted Answer

The graph of the prediction equation obtained from the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$ is a plane because it involves two predictor variables, $X_1$ and $ X_2$ which make it a two-dimensional space, and the response variable $y$ is the height of the plane above that space.

Question 15

Which of the following is not an assumption of the multiple linear regression model?

Accepted Answer

The level of measurement of the data for the dependent variable could be nominal, ordinal, interval, or ratio. The other assumptions listed (A, B, C, E) are all necessary assumptions for multiple linear regression.

Question 16

In multiple regression analysis,the explained sum of squares divided by the total sum of squares yields the __________.

Accepted Answer

The explained sum of squares divided by the total sum of squares yields the R², which measures the proportion of variance in the dependent variable that is predictable from the independent variables.

Question 17

Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

Accepted Answer

Squared terms and interaction terms in a multiple regression model often increase multicollinearity as they are highly correlated with the original independent variables.

Question 18

A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield ______ and _______ degrees of freedom,respectively,for regression (explained)and error.

Accepted Answer

df for regression is k = 3, and df for error = N − (k + 1) = 20 − (3 + 1) = 16

Question 19

It is appropriate to use an interaction variable if the relationship between the dependent variable and one of the independent variables depends on the value of the other independent variable.

Accepted Answer

This statement accurately describes when it is appropriate to use an interaction variable.

Question 20

The multiple coefficient of determination is the _______ divided by the total variation.

Accepted Answer

The multiple coefficient of determination, denoted by R-squared, is the ratio of the explained variation to the total variation. It represents the proportion of variance in the dependent variable that can be explained by the independent variables included in the model. Therefore, the correct choice is (C) Explained variation.

Quiz 15: Multiple Regression and Model Building

A partial F test is used to assess when at least one variable in a subset of squared and interaction variables in the multiple regression model is significant.

If it is desired to include marital status in a multiple regression model by using the categories single,married,separated,divorced,widowed,what will be the effect on the model?

In multiple regression analysis,which one of the following is the appropriate notation for error (residual) ?

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

In multiple regression analysis,the mean square regression divided by mean square error yields the _________.

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

The range of feasible values for the multiple coefficient of correlation is from ________.

The range of feasible values for the multiple coefficient of determination is from ________.

The mean square error of a multiple regression model with k independent variables and n observations is __________.

When using a multiple regression model,we assume that error terms (residuals) are distributed according to a(n) ________________ distribution.

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

Even when encountering extreme multicollinearity with the use of squared and interaction variables,t tests on the significance of individual independent variables is reliable.

The graph of the prediction equation obtained from the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$ Is a(n) __________.

Which of the following is not an assumption of the multiple linear regression model?

In multiple regression analysis,the explained sum of squares divided by the total sum of squares yields the __________.

Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield and _ degrees of freedom,respectively,for regression (explained) and error.

It is appropriate to use an interaction variable if the relationship between the dependent variable and one of the independent variables depends on the value of the other independent variable.

The multiple coefficient of determination is the _______ divided by the total variation.

Quiz 15: Multiple Regression and Model Building

A partial F test is used to assess when at least one variable in a subset of squared and interaction variables in the multiple regression model is significant.

If it is desired to include marital status in a multiple regression model by using the categories single,married,separated,divorced,widowed,what will be the effect on the model?

In multiple regression analysis,which one of the following is the appropriate notation for error (residual) ?

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

In multiple regression analysis,the mean square regression divided by mean square error yields the _________.

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R2.

The range of feasible values for the multiple coefficient of correlation is from ________.

The range of feasible values for the multiple coefficient of determination is from ________.

The mean square error of a multiple regression model with k independent variables and n observations is __________.

When using a multiple regression model,we assume that error terms (residuals) are distributed according to a(n) ________________ distribution.

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

Even when encountering extreme multicollinearity with the use of squared and interaction variables,t tests on the significance of individual independent variables is reliable.

The graph of the prediction equation obtained from the model y=β0+β1X1+β2X2+ε\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilony=β0​+β1​X1​+β2​X2​+ε Is a(n) __________.

Which of the following is not an assumption of the multiple linear regression model?

In multiple regression analysis,the explained sum of squares divided by the total sum of squares yields the __________.

Using squared and interaction variables in a multiple regression model results in extreme multicollinearity.

A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield ______ and _______ degrees of freedom,respectively,for regression (explained) and error.

It is appropriate to use an interaction variable if the relationship between the dependent variable and one of the independent variables depends on the value of the other independent variable.

The multiple coefficient of determination is the _______ divided by the total variation.

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

The graph of the prediction equation obtained from the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$ Is a(n) __________.

A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield and _ degrees of freedom,respectively,for regression (explained) and error.