Multiple Regression – 2

Quantitative Methods

1 / 10

The Durbin-Watson statistic for a regression model is calculated as 1.8. What does this value suggest about the autocorrelation of the residuals?

Positively autocorrelated

Negatively autocorrelated

Not autocorrelated

Cannot be determined without more information.

2 / 10

You are assessing the presence of multicollinearity in a regression model, and the variance inflation factor (VIF) for an independent variable is calculated as 2.5. What does this value suggest about multicollinearity?

High multicollinearity

Moderate multicollinearity

Low multicollinearity

Cannot be determined without more information.

3 / 10

In a regression model, the residual standard error (RSE) is calculated as 15. If the mean of the dependent variable is 60, what is the coefficient of variation (CV) for the model?

10%

15%

25%

30%

4 / 10

You are conducting a hypothesis test for the coefficient of the independent variable X1 in a regression model. The test yields a p-value of 0.028. If you are using a significance level of 0.05, what is your decision regarding the null hypothesis?

Reject the null hypothesis.

Fail to reject the null hypothesis.

Cannot be determined without more information

The null hypothesis is not related to p-values.

If the p-value (0.028) is less than the significance level (0.05), you would reject the null hypothesis. The p-value represents the probability of observing the data or more extreme values under the assumption that the null hypothesis is true. A p-value less than the significance level indicates that the observed results are statistically significant, and you have enough evidence to reject the null hypothesis.

5 / 10

In a regression model, if the p-value for the F-statistic is less than the significance level (e.g., 0.05), what does it suggest about the overall model?

The model is a good fit.

The model is not a good fit.

The model is overfit.

The model is not affected by multicollinearity.

6 / 10

What is the purpose of multicollinearity diagnostics in a regression analysis?

To check for normality of residuals

To assess the correlation between independent variables

To determine the strength of the relationship between dependent and independent variables

To check for heteroscedasticity

7 / 10

When conducting hypothesis tests on individual coefficients in a regression model, what is the null hypothesis typically?

The coefficient is equal to zero.

The coefficient is statistically significant.

The coefficient is negatively correlated with the dependent variable.

The coefficient is not relevant to the model.

8 / 10

In a regression model, if the Durbin-Watson statistic is close to 2, what does it suggest about the residuals?

The residuals are positively autocorrelated.

The residuals are negatively autocorrelated.

The residuals are not autocorrelated.

The residuals are heteroscedastic

9 / 10

If the p-value for a coefficient in a regression model is less than the significance level (e.g., 0.05), what does it indicate?

The coefficient is not statistically significant.

The coefficient is statistically significant.

The coefficient has a high correlation with the dependent variable.

The coefficient has a low R-squared value.

10 / 10

In multiple regression analysis, which of the following statistics measures the proportion of the variation in the dependent variable explained by the independent variables?

Standard error

Coefficient of determination (R-squared)

p-value

F-statistic

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