Which statistic is specifically used to test the overall fit of a regression model in simple and multiple regression?

Which statistic is specifically used to test the overall fit of a regression model in simple and multiple regression?

• A. F-statistic
• B. Eta squared (η2)
• C. Exp(B)
• D. Cross-sectional

Answer: (A)

The key idea is assessing the overall significance of a regression model using the F-statistic. In both simple and multiple regression, you want to know if the model explains more of the variation in the dependent variable than you would expect by chance. The F-statistic does this by comparing the variance explained by the model (the regression sum of squares) to the variance left unexplained (the residual sum of squares). A large F value with a small p-value means the null hypothesis — that all the regression coefficients are zero (no linear relationship between predictors and outcome) — can be rejected. In other words, the model provides a meaningful improvement over just using the mean. Eta squared is an effect size measure that tells you how much of the variance is explained, but it doesn’t test that the model as a whole is significant. Exp(B) is the odds ratio from logistic regression, not the test of overall fit in linear regression. Cross-sectional refers to a study design, not a statistic.

The key idea is assessing the overall significance of a regression model using the F-statistic. In both simple and multiple regression, you want to know if the model explains more of the variation in the dependent variable than you would expect by chance. The F-statistic does this by comparing the variance explained by the model (the regression sum of squares) to the variance left unexplained (the residual sum of squares). A large F value with a small p-value means the null hypothesis — that all the regression coefficients are zero (no linear relationship between predictors and outcome) — can be rejected. In other words, the model provides a meaningful improvement over just using the mean.

Eta squared is an effect size measure that tells you how much of the variance is explained, but it doesn’t test that the model as a whole is significant. Exp(B) is the odds ratio from logistic regression, not the test of overall fit in linear regression. Cross-sectional refers to a study design, not a statistic.