Factors Affecting Standard Error of the Slope

Question

The formula for the standard error of a regression slope is $$s_b = \frac{s}{s_x\sqrt{n-1}}$$. Rank the following factors, which are considered individually, in order of their impact on decreasing the value of $$s_b$$, from greatest to least: (i) a decrease in the residual standard error, $$s$$; (ii) an increase in the standard deviation of the x-values, $$s_x$$; (iii) an increase in the sample size, $$n$$; and (iv) a change in the y-intercept.

Accepted Answer

A decrease in the residual standard error, An increase in the spread of the x-values, An increase in the sample size, Any change in the y-intercept

Answer

An increase in the sample size, An increase in the spread of the x-values, A decrease in the residual standard error, Any change in the y-intercept

Answer

Any change in the y-intercept, A decrease in the residual standard error, An increase in the spread of the x-values, An increase in the sample size

Answer

An increase in the spread of the x-values, A decrease in the residual standard error, An increase in the sample size, Any change in the y-intercept

Factors Affecting Standard Error of the Slope

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