Question 1

Which one of the following tools is not used to check the normality of residuals assumption for a multiple regression model?

Accepted Answer

Scatter diagram is not used to check the normality of residuals assumption for a multiple regression model. Scatter diagram is used to check the linearity assumption of the regression model. Histogram, stem-and-leaf display, and normal plot are commonly used to check the normality assumption of the residuals in a multiple regression model.

Question 2

R² is defined as:

Accepted Answer

R², or the coefficient of determination, is defined as the ratio of explained variation to total variation in a regression model.

Question 3

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n)____________.

Accepted Answer

Dummy (indicator) variables are used to model the effects of different levels of a qualitative independent variable in multiple regression analysis. The use of indicator variables allows us to include categorical variables in the regression model as continuous variables, thereby enabling us to estimate the effect of each level of the variable relative to a reference level.

Question 4

If we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁ = 0,we conclude that:

Accepted Answer

If we reject the null hypothesis that β₁ = 0, it implies that X₁ is significantly related to y. Thus, option A is the correct answer.

Question 5

The general form of the quadratic multiple regression models is:

Accepted Answer

The answer of The general form of the quadratic multiple...

Question 6

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of ___________ variables.

Accepted Answer

Dummy or indicator variables are used to model the effects of different levels of qualitative variables. Quantitative, ratio and measured variables are not appropriate for dummy coding.

Question 7

In a multiple regression model,the residuals were plotted against the values of one of the independent variables.The plot exhibited a funneling out pattern of residuals.This means that as the value of the independent variable increases,the error terms tend to ___________ and the model assumption of __________ is violated.

Accepted Answer

The funneling out pattern of residuals indicates that as the value of the independent variable increases, the error terms tend to increase as well, violating the assumption of constant variance (also known as homoscedasticity). This suggests that there may be some unaccounted for variables that are related to the variance of the error terms, and the model may need to be adjusted accordingly.

Question 8

Assumptions of a regression model can be evaluated by plotting and analyzing the ____________.

Accepted Answer

Assumptions of a regression model can be evaluated by plotting and analyzing the error terms or residuals. One can check if the residuals are normally distributed, have constant variance, and are independent of each other. These checks help in assessing if the regression model is appropriate for the data and if the results can be trusted.

Question 9

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

Accepted Answer

The standard error of the estimate is never greater than the standard deviation of the dependent variable because it measures the spread of the residuals around the regression line, which is always less than or equal to the spread of the actual data points around their mean.

Question 10

The multiple _________ measures the proportion of the variation in y (response variable)explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

Accepted Answer

The coefficient of determination, also known as R-squared, measures how much of the variability in the response variable is explained by the independent variables in the multiple regression model. It ranges between 0 and 1, with higher values indicating a better fit of the model to the data.

Question 11

Dummy variables take on the values of _________ and are used to model the effects of different levels of qualitative variables.

Accepted Answer

Dummy variables take on the values of 0 or 1, indicating the absence or presence of a particular feature or category. For example, if we are creating a dummy variable for gender, the possible values would be 0 for male and 1 for female. This allows us to model the effects of different levels of qualitative variables in a regression analysis.

Question 12

The ____________ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

Accepted Answer

The error term represents the variability in y that is not explained by the independent variables in the model. It includes the effects of any omitted variables, measurement error, or random variation in the data.

Question 13

In a multiple regression analysis,if the normal probability plot ____________,then it can be concluded that the assumption of normality is not violated.

Accepted Answer

If the normal probability plot is a straight line, it indicates that the residuals (the differences between the observed values and the predicted values) are normally distributed, and therefore, the assumption of normality is not violated. A curved plot or skewness in the plot indicates a violation of the normality assumption. The shape of the plot opening upward as a parabola is never observed in a normal probability plot.

Question 14

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

Accepted Answer

A desirable residual plot has a horizontal band appearance, indicating that the residuals have a constant variance and are normally distributed. Curved or cyclical patterns suggest that the model is not capturing all of the relevant information, while fanning out or funneling in patterns suggest that the error variance changes as the predicted values change.

Question 15

Plotting the residuals in a time-ordered sequence will reveal possible violations of the __________ of error terms assumption.

Accepted Answer

Plotting residuals in a time-ordered sequence helps to assess the independence assumption. If the residuals show correlation or patterns over time, it indicates that the model does not capture all the relevant information or that the errors are not independent. Normality and constant variation assumptions can be assessed through normal probability plots and plots of residuals against predicted values, respectively. Residual sum is not an assumption but a measure of the difference between actual and predicted values.

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 it implies that the model perfectly fits the data, which is unlikely to happen in practice. Instead, we expect the residuals to have a mean of zero, constant variance, be independent, and follow a normal distribution.

Question 17

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

Accepted Answer

Residuals vs. parameter estimates is not a common type of residual plot used in regression analysis. The other four options (B, C, D, and E) are all commonly used residual plots.

Question 18

An acceptable residual plot exhibits:

Accepted Answer

A residual plot with constant error variance indicates that the model is making consistent errors across the range of predictors. This is desirable because it suggests that the model is not biased towards any particular part of the data and is capturing the variability in the data appropriately.

Question 19

The y intercept (β₀)in a multiple regression model represents the estimated value of the __________ variable,when the value of all independent variables are _________.

Accepted Answer

The y intercept (β₀) represents the estimated value of the response variable when all independent variables have a value of zero. Therefore, the correct choice is C - the y intercept represents the estimated value of the response variable with all independent variables at zero.

Question 20

The effects of different levels of qualitative independent variables are described using ___________ variables.

Accepted Answer

The effects of different levels of qualitative independent variables are typically described using dummy variables, which are used to represent different categories of the qualitative independent variable in regression analysis.

Quiz 15: Multiple Regression and Model Building

Which one of the following tools is not used to check the normality of residuals assumption for a multiple regression model?

R² is defined as:

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n) ____________.

If we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁ = 0,we conclude that:

The general form of the quadratic multiple regression models is:

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of ___________ variables.

Assumptions of a regression model can be evaluated by plotting and analyzing the ____________.

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

The multiple _________ measures the proportion of the variation in y (response variable) explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

Dummy variables take on the values of _________ and are used to model the effects of different levels of qualitative variables.

The ____________ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

In a multiple regression analysis,if the normal probability plot ____________,then it can be concluded that the assumption of normality is not violated.

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

Plotting the residuals in a time-ordered sequence will reveal possible violations of the __________ of error terms assumption.

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

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

An acceptable residual plot exhibits:

The y intercept (β₀) in a multiple regression model represents the estimated value of the __ variable,when the value of all independent variables are _.

The effects of different levels of qualitative independent variables are described using ___________ variables.

Quiz 15: Multiple Regression and Model Building

Which one of the following tools is not used to check the normality of residuals assumption for a multiple regression model?

R2 is defined as:

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n) ____________.

If we are testing the significance of the independent variable X1 and we reject the null hypothesis H0: β1 = 0,we conclude that:

The general form of the quadratic multiple regression models is:

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of ___________ variables.

Assumptions of a regression model can be evaluated by plotting and analyzing the ____________.

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

The multiple _________ measures the proportion of the variation in y (response variable) explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

Dummy variables take on the values of _________ and are used to model the effects of different levels of qualitative variables.

The ____________ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

In a multiple regression analysis,if the normal probability plot ____________,then it can be concluded that the assumption of normality is not violated.

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

Plotting the residuals in a time-ordered sequence will reveal possible violations of the __________ of error terms assumption.

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

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

An acceptable residual plot exhibits:

The y intercept (β0) in a multiple regression model represents the estimated value of the __________ variable,when the value of all independent variables are _________.

The effects of different levels of qualitative independent variables are described using ___________ variables.

R² is defined as:

If we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: β₁ = 0,we conclude that:

The y intercept (β₀) in a multiple regression model represents the estimated value of the __ variable,when the value of all independent variables are _.