Question 1

The assumption of independent error terms in regression analysis is often violated when using time-series data.

Accepted Answer

In time-series data, errors are often correlated across time points, violating the assumption of independent error terms. This can lead to biased estimates and inaccurate hypothesis testing.

Question 2

If we are predicting y when the values of the independent variables are x₀₁,x₀₂,... ,x₀_k,the farther the values of x₀₁,x₀₂,... ,x₀_kare from the center of the observed data,the smaller the distance value and the more precise the associated confidence and prediction intervals.

Accepted Answer

The farther the values are from the center, then the larger the distance value, and both the confidence interval and prediction interval are wider.

Question 3

Testing the contribution of individual independent variables with ttests is performed prior to the Ftest for the model in multiple regression analysis.

Accepted Answer

An F test is performed first to determine whether there is a reason to do individual t-tests.

Question 4

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

Accepted Answer

The error term captures the effects of all other factors that are not accounted for by the independent variables in predicting the response variable y. It represents the variability in y that cannot be explained by the model.

Question 5

In a multiple regression mode,if the largest variance inflation factor (VIF)is 21.6,then it can be concluded that there are indications of multicollinearity.

Accepted Answer

A VIF of 21.6 is considered very high and indicates a strong presence of multicollinearity among the predictor variables in the multiple regression model.

Question 6

The multiple correlation coefficient can assume any value between zero and 1,inclusive.

Accepted Answer

The multiple correlation coefficient has values between −1 and +1.

Question 7

When the F test is used to test the overall significance of a multiple regression model,if the null hypothesis is rejected,it can be concluded that all of the independent variables x₁,x₂,... ,x_k are significantly related to the dependent variable y.

Accepted Answer

Rejecting the null hypothesis in an F test for a multiple regression model indicates that at least one of the independent variables is significantly related to the dependent variable, not necessarily all of them.

Question 8

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

Accepted Answer

If the normal probability plot exhibits a straight line, it indicates that the residuals follow a normal distribution and the assumption of normality is not violated.

Question 9

In comparing regression models,the regression model with the largest R²will also have the smallest standard error (s).

Accepted Answer

Standard error only decreases if the adjusted R² increases. So if comparing regression models, you should use adjusted R² rather than R².

Question 10

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

Accepted Answer

The variance inflation factor (VIF) measures the degree of multicollinearity (correlation among independent variables) in a regression model, not the relationship between the dependent variable and the independent variables.

Question 11

When the quadratic regression model y = β₀ + β₁x + β₂x² + ε is used,the term β₁shows the rate of curvature of the parabola.

Accepted Answer

The term β₁shows the shift of the parameter.

Question 12

Because multiple regression models consist of multiple independent variables,residual analysis cannot be performed.

Accepted Answer

Residual analysis can and should be performed on multiple regression models to check for assumptions and evaluate model fit.

Question 13

A ttest is used in testing the significance of an individual independent variable.

Accepted Answer

For testing the significance of any independent variable, use a t-test.

Question 14

For the same point estimate of the dependent variable and the same level of significance,the confidence interval is always wider than the corresponding prediction interval.

Accepted Answer

Confidence intervals are always narrower than the corresponding prediction interval.

Question 15

Even when an unimportant variable is added to a regression model,the explained variation will increase.

Accepted Answer

Adding any variable to a regression model will increase the total explained variation (sum of squares), even if it is not a significant predictor. However, this does not necessarily mean that the additional variable improves the model's predictive power or adds meaningful information. This is why it's important to evaluate the statistical significance and practical relevance of each variable in a regression model.

Question 16

The normal plot is a residual plot that checks the normality assumption.

Accepted Answer

The normal plot, also known as a Q-Q plot, is a plot that compares the distribution of the residuals to a normal distribution. It is used to check the normality assumption in linear regression models.

Question 17

In a regression model,a value of the error term depends upon other values of the error term.

Accepted Answer

Error terms are statistically independent of each other.

Question 18

Regression models that employ more than one independent variable are referred to as multiple regression models.

Accepted Answer

Multiple regression models use more than one independent variable to predict a dependent variable.

Question 19

In a regression model,at any given combination of values of the independent variables,the population of potential error terms is assumed to have an F distribution.

Accepted Answer

In a regression model, at any given combination of values of the independent variables, the population of potential error terms is assumed to have a normal distribution, not an F distribution. The F distribution is used in hypothesis testing for the significance of the overall regression model and individual coefficients.

Question 20

An application of the multiple regression model generated the following results involving the F test of the overall regression model:p-value= .0012,R² = .67,and s = .076.Thus,the null hypothesis,which states that none of the independent variables are significantly related to the dependent variable,should be rejected at the .05 level of significance.

Accepted Answer

The p-value of .0012 is less than .05, indicating that the overall regression model is statistically significant. Therefore, the null hypothesis should be rejected and it can be concluded that at least one independent variable is significantly related to the dependent variable.

Quiz 14: Simple Linear Regression Analysis