Question 1

In a simple linear regression model,testing whether the slope $\beta _ { 1 }$ 
of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

Accepted Answer

Testing whether the slope $\beta_1$ is zero is equivalent to testing if there is a significant linear relationship between X and Y, as a zero slope indicates no linear relationship.

Question 2

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of Y,then look for a change in the spread of the plotted values.

Accepted Answer

This is a common method of diagnosing heteroscedasticity in regression analysis.

Question 3

In regression analysis,homoscedasticity refers to constant error variance.

Accepted Answer

Homoscedasticity means that the variance of errors is constant across all levels of the predictor variable. This is important in regression analysis as it ensures that the model assumptions are met, leading to more accurate and reliable results.

Question 4

In testing the overall fit of a multiple regression model in which there are three explanatory variables,the null hypothesis is $H _ { 0 } : B _ { 1 } = B _ { 2 } = B _ { 3 }$ 
.

Accepted Answer

The null hypothesis for testing the overall fit of a multiple regression model is $H_0: B_1 = B_2 = B_3 = 0$, which tests if all the coefficients are equal to zero, indicating no relationship between the explanatory variables and the dependent variable.

Question 5

The residuals are observations of the error variable $\varepsilon$ 
.Consequently,the minimized sum of squared deviations is called the sum of squared error,labeled SSE.

Accepted Answer

Residuals are estimates of the error term $\varepsilon$ in a regression model, and the sum of squared residuals is often referred to as the sum of squared errors (SSE).

Question 6

The Durbin-Watson statistic can be used to measure of autocorrelation.

Accepted Answer

The Durbin-Watson statistic is designed to detect autocorrelation in a regression analysis.

Question 7

The value of the sum of squares due to regression,SSR,can never be larger than the value of the sum of squares total,SST.

Accepted Answer

This statement is true. The sum of squares total (SST) represents the total variation in the response variable, while the sum of squares due to regression (SSR) represents the variation in the response variable that is explained by the regression model. Since the regression model explains some but not all of the total variation in the response variable, SSR must always be less than or equal to SST. Mathematically,

SST = SSE + SSR

where SSE is the sum of squares due to error. Since SSE is always positive, it follows that SSR <= SST.

Question 8

Homoscedasticity means that the variability of Y values is the same for all X values.

Accepted Answer

Homoscedasticity means that the variance of the errors of a regression model is the same for all values of the independent variable. This implies that the variability of Y values is the same for all X values. Therefore, the statement is true.

Question 9

A confidence interval constructed around a point prediction from a regression model is called a prediction interval,because the actual point being estimated is not a population parameter

Accepted Answer

A confidence interval around a point prediction is called a prediction interval, as it accounts for the additional uncertainty associated with making predictions for individual data points rather than estimating population parameters.

Question 10

Which of the following would be considered a definition of an outlier?

Accepted Answer

An outlier is defined as an unusual or extreme value that does not follow the general pattern or distribution of the other observations. It can be identified by being an extreme value for one or more variables, having a residual that is abnormally large in magnitude, or having values for individual explanatory variables that fall outside the general pattern of the other observations. Only option D includes all of these criteria, therefore it is the best choice.

Question 11

When determining whether to include or exclude a variable in regression analysis,if the p-value associated with the variable's t-value is above some accepted significance value,such as 0.05,then the variable:

Accepted Answer

If the p-value associated with the variable's t-value is above the accepted significance value, then there is not enough evidence to suggest that the variable has a significant effect on the outcome. Therefore, it is a candidate for exclusion from the regression analysis.

Question 12

The assumptions of regression are: 1)there is a population regression line,2)the dependent variable is normally distributed,3)the standard deviation of the response variable remains constant as the explanatory variables increase,and 4)the errors are probabilistically independent.

Accepted Answer

These are the four assumptions of linear regression.

Question 13

Which of the following is not one of the guidelines for including/excluding variables in a regression equation?

Accepted Answer

The answer of Which of the following is not one...

Question 14

A backward procedure is a type of equation building procedure that begins with all potential explanatory variables in the regression equation and deletes them two at a time until further deletion would reduce the percentage of variation explained to a value less than 0.50.

Accepted Answer

A backward procedure starts with all potential explanatory variables in the regression equation and eliminates them one at a time until a stopping criterion is met, such as a certain level of statistical significance or a decrease in the percentage of variance explained.

Question 15

A scatterplot that exhibits a "fan" shape (the variation of Y increases as X increases)is an example of:

Accepted Answer

The answer of A scatterplot that exhibits a "fan" shape...

Question 16

Suppose you run a regression of a person's height on his/her right and left foot sizes,and you suspect that there may be multicollinearity between the foot sizes.What types of problems might you see if your suspicions are true?

Accepted Answer

Multicollinearity can lead to incorrect coefficient estimates, which can be identified by wrong values, large p-values, or small t-values. Therefore, all of the options (A, B, and C) are correct.

Question 17

In multiple regressions,a large value of the test statistic F indicates that most of the variation in Y is unexplained by the regression equation and that the model is useless.A small value of F indicates that most of the variation in Y is explained by the regression equation and that the model is useful.

Accepted Answer

The statement is not true. A large value of the test statistic F actually indicates that most of the variation in Y is explained by the regression equation and that the model is useful. Conversely, a small value of F indicates that most of the variation in Y is unexplained by the regression equation and that the model may not be useful.

Question 18

The can be used to test for autocorrelation.

Accepted Answer

The Durbin-Watson statistic is a test for autocorrelation, which is the correlation of a variable with its lagged values. It measures the degree to which adjacent observations in a time series are correlated with each other. If the DW statistic is close to 2, there is no autocorrelation. If it is significantly less than 2, then there is positive autocorrelation, and if it is significantly greater than 2, then there is negative autocorrelation. Therefore, option C is the best choice.

Question 19

In regression analysis,the unexplained part of the total variation in the response variable Y is referred to as sum of squares due to regression,SSR.

Accepted Answer

The unexplained part of the total variation in the response variable Y is referred to as sum of squares error, SSE. The sum of squares due to regression, SSR, represents the explained variation in Y due to the regression model.

Question 20

A forward procedure is a type of equation building procedure that begins with only one explanatory variable in the regression equation and successively adds one variable at a time until no remaining variables make a significant contribution.

Accepted Answer

The answer of A forward procedure is a type of...

Quiz 11: Regression Analysis: Statistical Inference

In a simple linear regression model,testing whether the slope $\beta _ { 1 }$ of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of Y,then look for a change in the spread of the plotted values.

In regression analysis,homoscedasticity refers to constant error variance.

In testing the overall fit of a multiple regression model in which there are three explanatory variables,the null hypothesis is $H _ { 0 } : B _ { 1 } = B _ { 2 } = B _ { 3 }$ .

The residuals are observations of the error variable $\varepsilon$ .Consequently,the minimized sum of squared deviations is called the sum of squared error,labeled SSE.

The Durbin-Watson statistic can be used to measure of autocorrelation.

The value of the sum of squares due to regression,SSR,can never be larger than the value of the sum of squares total,SST.

Homoscedasticity means that the variability of Y values is the same for all X values.

A confidence interval constructed around a point prediction from a regression model is called a prediction interval,because the actual point being estimated is not a population parameter

Which of the following would be considered a definition of an outlier?

When determining whether to include or exclude a variable in regression analysis,if the p-value associated with the variable's t-value is above some accepted significance value,such as 0.05,then the variable:

The assumptions of regression are: 1)there is a population regression line,2)the dependent variable is normally distributed,3)the standard deviation of the response variable remains constant as the explanatory variables increase,and 4)the errors are probabilistically independent.

Which of the following is not one of the guidelines for including/excluding variables in a regression equation?

A backward procedure is a type of equation building procedure that begins with all potential explanatory variables in the regression equation and deletes them two at a time until further deletion would reduce the percentage of variation explained to a value less than 0.50.

A scatterplot that exhibits a "fan" shape (the variation of Y increases as X increases) is an example of:

Suppose you run a regression of a person's height on his/her right and left foot sizes,and you suspect that there may be multicollinearity between the foot sizes.What types of problems might you see if your suspicions are true?

The can be used to test for autocorrelation.

In regression analysis,the unexplained part of the total variation in the response variable Y is referred to as sum of squares due to regression,SSR.

A forward procedure is a type of equation building procedure that begins with only one explanatory variable in the regression equation and successively adds one variable at a time until no remaining variables make a significant contribution.

Quiz 11: Regression Analysis: Statistical Inference

In a simple linear regression model,testing whether the slope β1\beta _ { 1 }β1​ of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of Y,then look for a change in the spread of the plotted values.

In regression analysis,homoscedasticity refers to constant error variance.

In testing the overall fit of a multiple regression model in which there are three explanatory variables,the null hypothesis is H0:B1=B2=B3H _ { 0 } : B _ { 1 } = B _ { 2 } = B _ { 3 }H0​:B1​=B2​=B3​ .

The residuals are observations of the error variable ε\varepsilonε .Consequently,the minimized sum of squared deviations is called the sum of squared error,labeled SSE.

The Durbin-Watson statistic can be used to measure of autocorrelation.

The value of the sum of squares due to regression,SSR,can never be larger than the value of the sum of squares total,SST.

Homoscedasticity means that the variability of Y values is the same for all X values.

A confidence interval constructed around a point prediction from a regression model is called a prediction interval,because the actual point being estimated is not a population parameter

Which of the following would be considered a definition of an outlier?

When determining whether to include or exclude a variable in regression analysis,if the p-value associated with the variable's t-value is above some accepted significance value,such as 0.05,then the variable:

The assumptions of regression are: 1)there is a population regression line,2)the dependent variable is normally distributed,3)the standard deviation of the response variable remains constant as the explanatory variables increase,and 4)the errors are probabilistically independent.

Which of the following is not one of the guidelines for including/excluding variables in a regression equation?

A backward procedure is a type of equation building procedure that begins with all potential explanatory variables in the regression equation and deletes them two at a time until further deletion would reduce the percentage of variation explained to a value less than 0.50.

A scatterplot that exhibits a "fan" shape (the variation of Y increases as X increases) is an example of:

Suppose you run a regression of a person's height on his/her right and left foot sizes,and you suspect that there may be multicollinearity between the foot sizes.What types of problems might you see if your suspicions are true?

The can be used to test for autocorrelation.

In regression analysis,the unexplained part of the total variation in the response variable Y is referred to as sum of squares due to regression,SSR.

A forward procedure is a type of equation building procedure that begins with only one explanatory variable in the regression equation and successively adds one variable at a time until no remaining variables make a significant contribution.

In a simple linear regression model,testing whether the slope $\beta _ { 1 }$ of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

In testing the overall fit of a multiple regression model in which there are three explanatory variables,the null hypothesis is $H _ { 0 } : B _ { 1 } = B _ { 2 } = B _ { 3 }$ .

The residuals are observations of the error variable $\varepsilon$ .Consequently,the minimized sum of squared deviations is called the sum of squared error,labeled SSE.