Question

In linear regression, mean squared regression (effect variance) divided by mean squared error (error variance) is called the:

• A. p-value.
• B. F-statistic.
• C. t-statistic.
• D. R-squared value.

Hint:

To understand regression statistics:
1. The F-statistic evaluates the overall significance of the regression model.
2. The t-statistic tests individual coefficients, while the R-squared value measures goodness-of-fit.
3. The p-value provides evidence against the null hypothesis.

Answer 1

The Correct Option is B

Step 1: Understand the F-statistic in linear regression. The F-statistic in linear regression is a ratio that measures the proportion of the explained variance (mean squared regression) relative to the unexplained variance (mean squared error). It is calculated as: \[ F = \frac{\text{Mean Squared Regression (MSR)}}{\text{Mean Squared Error (MSE)}}. \] The F-statistic tests the null hypothesis that all regression coefficients (except the intercept) are equal to zero. A higher F-value indicates a stronger relationship between the predictor variables and the response variable. Step 2: Evaluate the options. Option (A): Incorrect. The p-value is a probability that measures the strength of evidence against the null hypothesis. It is not calculated as a ratio of MSR to MSE.
Option (B): Correct. The F-statistic is defined as the ratio of MSR to MSE in linear regression.
Option (C): Incorrect. The t-statistic is used to test individual regression coefficients, not the overall model fit, and it is not the ratio of MSR to MSE.
Option (D): Incorrect. The R-squared value measures the proportion of variance in the dependent variable explained by the independent variables but is not calculated as MSR divided by MSE.