Multiple Linear Regression

Which of the following is a key assumption of multiple linear regression?

• Heteroskedasticity of residuals.

• Dependence between the dependent variable and residuals.

• Non-linearity in the relationship between variables.

• None of the above.

What is multicollinearity in the context of multiple linear regression?

• The presence of multiple correlated outliers in the independent variables.

• High correlation between two or more independent variables.

• The lack of correlation between the dependent variable and independent variables.

• The presence of a normal distribution of multiple residuals.

What distinguishes hierarchical multiple linear regression from simple multiple linear regression?

• It involves the use of multiple independent variables.

• It enters the predictor variables into the model in stages or blocks.

• It focuses on predicting categorical outcome.

• It involves the use of multiple dependent variables.

What are the hypotheses when testing whether the predictor variable in a multiple linear regression model significantly predict the dependent variable?

• H0: βi > 0​

  H1: βi < 0​

• H0: βi < 0​

  H1: βi > 0​

• H0: βi ≠ 0​

  H1: βi = 0​

• H0: βi = 0​

  H1: βi ≠ 0​

Which of the following statements is true regarding the assumption of normality in multiple linear regression?

• The assumption of normality only applies to the dependent variable.

• The assumption of normality is not relevant in multiple linear regression.

• The normality assumption pertains to the residuals, not the independent variables.

• Normality is a requirement for the predictor variables, not the residuals.

If the residuals in a multiple linear regression analysis are not normally distributed, what potential issues might arise?

• The model will be biased, affecting the accuracy of predictions.

• It may lead to multicollinearity among the independent variables.

• Non-normal residuals have no impact on the validity of the model.

• It only affects the precision of the estimated coefficients.

A significant F found in the ANOVA table, when doing Multiple Linear Regression, indicates which of the following outcomes?

• Changes in the dependent variable cannot be explained by changes in the independent variables.

• The regression equation can accurately explain variation in the dependent variable.

• The ratio of the mean square terms is equal to 0.

• Only one of the independent variables significantly contributes to the regression model.

The coefficient of determination (R2) is the proportion of variance in the independent variable that is explained by the dependent variables.

• True

• False