Question 1

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 (MSR/MSE) is the F statistic in multiple regression analysis. It is used to test whether at least one of the independent variables has a significant effect on the dependent variable. Therefore, the best choice is B, the F statistic.

Question 2

Which of the following residual plots is not used in regression analysis?

Accepted Answer

Residuals vs. parameter estimates is not a common residual plot in regression analysis. The other four plots are commonly used to assess the assumptions of linear regression.

Question 3

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

The degrees of freedom for regression is the number of independent variables, which is 3. The degrees of freedom for error is the number of observations minus the number of independent variables minus 1, which is 20 - 3 - 1 = 16.

Question 4

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 5

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

Accepted Answer

The multiple coefficient of determination is calculated by dividing the explained variation by the total variation. The explained variation is the variation that is accounted for by the model, whereas the total variation is the variance of the dependent variable. Therefore, choice C is the correct answer.

Question 6

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

Accepted Answer

The appropriate notation for error (residual) in multiple regression analysis is usually represented by the letter "e" followed by a subscript indicating the observation number. Choice B includes "e" followed by a unique code indicating the observation number, making it the most appropriate notation.

Question 7

In multiple regression analysis,a desirable residual plot has what type of appearance?

Accepted Answer

A horizontal band is the desired residual plot in multiple regression analysis.

Question 8

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 variable is negative (-4.2), indicating that females earn less than males. Since the salaries are in thousands of dollars, a coefficient of -4.2 means that, on average, females earn $4,200 less than males. The significance of the variable at α=0.1 means that there is strong evidence that the gender variable is associated with salary, with a low probability of this result occurring by chance.

Question 9

An acceptable residual plot exhibits

Accepted Answer

A residual plot with constant error variance indicates that the model's predictions have consistent accuracy throughout the range of predictor values. This is preferred over increasing or decreasing error variance, which would suggest that the model is systematically overestimating or underestimating the outcome variable. A curved pattern or a mixture of increasing and decreasing error variance would also suggest that the model may not be capturing the true relationship between the predictor and outcome variables.

Question 10

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₂ + ε is a(n)__________.

Accepted Answer

Two independent variables indicate the graph of a plane.

Question 11

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

Accepted Answer

The answer of In multiple regression analysis,the explained sum of...

Question 12

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.

Question 13

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 linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. The value cannot be less than -1 or greater than 1.

Question 14

is defined as

Accepted Answer

The ratio of explained variation (the variation accounted for by the model) to total variation (the overall variation in the data) is known as the coefficient of determination or R-squared. Therefore, the correct option is "explained variation/total variation."

Question 15

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

Accepted Answer

In multiple regression, we assume that the error terms (residuals) are normally distributed. This assumption is important for making statistical inferences and predictions based on the model. Other distributions, such as binomial, exponential, and Poisson, are not typically used in multiple regression models.

Question 16

Which one of the following is not an assumption about the residuals in a regression model?

Accepted Answer

The variance of the residuals should not be zero, as this would imply that the model perfectly predicts the outcome variable, which is unlikely to be the case in real-world data.

Question 17

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

Accepted Answer

The multiple coefficient of determination (R-squared) ranges from 0 (no linear relationship between the dependent and independent variables) to 1 (perfect linear relationship). Negative values are not possible as they would indicate a worse fit than no relationship. Therefore, the only feasible range for R-squared is 0 to 1, making option D the correct choice.

Question 18

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 is not an assumption of the multiple linear regression model. The other assumptions listed (independent error terms, normal distribution of error terms, equal variances of error terms, and zero mean of potential error terms) are all necessary assumptions of the model.

Question 19

In regression analysis,the standard error(s)is _________ greater than the standard deviation of y (the dependent variable).

Accepted Answer

Because standard deviation is divided by sample size to obtain standard error, standard deviation can never be smaller than standard error.

Question 20

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

Accepted Answer

For n categories, there will be n - 1 independent variables in a multiple regression model.

Quiz 14: Simple Linear Regression Analysis

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

Which of the following residual plots is not used in regression analysis?

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.

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

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

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

In multiple regression analysis,a desirable residual plot has what type of appearance?

An acceptable residual plot exhibits

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₂ + ε is a(n) __________.

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

is defined as

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

Which one of the following is not an assumption about the residuals in a regression model?

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

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

In regression analysis,the standard error(s) is _________ greater than the standard deviation of y (the dependent variable) .

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

Quiz 14: Simple Linear Regression Analysis

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

Which of the following residual plots is not used in regression analysis?

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.

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

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

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

In multiple regression analysis,a desirable residual plot has what type of appearance?

An acceptable residual plot exhibits

The graph of the prediction equation obtained from the model y = β0 + β1X1 + β2X2 + ε is a(n) __________.

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

is defined as

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

Which one of the following is not an assumption about the residuals in a regression model?

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

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

In regression analysis,the standard error(s) is _________ greater than the standard deviation of y (the dependent variable) .

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

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.

The graph of the prediction equation obtained from the model y = β₀ + β₁X₁ + β₂X₂ + ε is a(n) __________.

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