In regression results, which statement correctly characterizes the role of the t-statistic for the slope?

In regression results, which statement correctly characterizes the role of the t-statistic for the slope?

• A. The t-statistic tests whether the intercept is significantly different from zero
• B. The t-statistic tests whether the residuals are heteroscedastic
• C. The t-statistic tests the overall model significance
• D. The t-statistic tests whether the slope is significantly different from zero

Answer: (D)

In regression analysis, the t-statistic for the slope assesses whether the slope is significantly different from zero. The slope measures how much the response changes with a one-unit change in the predictor, so a slope not equal to zero indicates a real relationship rather than no relationship. The t-statistic is the estimated slope divided by its standard error, and if this value is large in absolute terms (yielding a small p-value), you conclude that the predictor contributes meaningfully to explaining the response. This is the specific test used to decide if the predictor’s effect is statistically detectable, given the sample data and assumptions (like normally distributed errors with constant variance). The intercept has its own separate test to see if it differs from zero, the overall model’s significance is typically assessed with an F-statistic, and diagnostics for heteroscedasticity involve other methods, not the slope’s t-test.

In regression analysis, the t-statistic for the slope assesses whether the slope is significantly different from zero. The slope measures how much the response changes with a one-unit change in the predictor, so a slope not equal to zero indicates a real relationship rather than no relationship. The t-statistic is the estimated slope divided by its standard error, and if this value is large in absolute terms (yielding a small p-value), you conclude that the predictor contributes meaningfully to explaining the response. This is the specific test used to decide if the predictor’s effect is statistically detectable, given the sample data and assumptions (like normally distributed errors with constant variance). The intercept has its own separate test to see if it differs from zero, the overall model’s significance is typically assessed with an F-statistic, and diagnostics for heteroscedasticity involve other methods, not the slope’s t-test.