Normality Condition For Regression Slope Inference
A regression analysis is conducted on the relationship between weekly study sessions (x) and test score improvement (y). The t-statistic for the slope is calculated using the formula . If the condition that the residuals are normally distributed is violated, what is the primary consequence for inference on the slope?
Non-normally distributed residuals weaken the validity of the t-test and confidence intervals because the assumed t-distribution of the statistic is no longer appropriate.
Non-normal residuals will lead to a slight change in the numerical value of the t-statistic but not enough to impact conclusions drawn from the test.
The t-test remains valid regardless of the residual distribution because the central limit theorem fully compensates for non-normal errors.
A departure from normality in residuals would affect only the intercept estimation, leaving the slope test unaffected.
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