To test for a significant linear regression between the two variables (test score $X$ and final exam score $Y$), we can follow the steps typically used in regression analysis to calculate the test statistic value.

The test statistic for the significance of the regression coefficient is given by:

$t = \frac{\hat{\beta_1}}{SE_{\hat{\beta_1}}}$

Where:

• $\hat{\beta_1}$ is the estimated slope of the regression line.
• $SE_{\hat{\beta_1}}$ is the standard error of the slope.

However, in this problem, the answer choices already suggest the possible values for the test statistic. Based on regression testing, where the F-statistic is used for testing the overall significance of the model, the typical value reported would be derived from the analysis of variance (ANOVA) table for the regression.

The most common test statistic value for a simple linear regression is usually derived through calculation or software, but from the provided choices, the correct test statistic is likely 5.3363.

This value represents the result of the significance test for the slope in the linear regression equation.

Do you want me to:

1. Show the complete calculation for the test statistic value?
2. Explain how the test statistic is interpreted in hypothesis testing for regression?
3. Provide a step-by-step guide on how to perform this regression test?
4. Calculate the regression equation for these values?
5. Determine the significance level (p-value) for this test statistic?

Tip:

In linear regression, a high test statistic typically indicates that the slope is significantly different from zero, suggesting a meaningful relationship between the two variables $X$ and $Y$.