# Question: The formula for the standard error of the sample slope

The formula for the standard error of the sample slope b is se = s/∑(x - )2, where s is the residual standard deviation of y.

a. Show that the smaller the value of s, the more precisely b estimates β.

b. Explain why a small s occurs when the data points show little variability about the prediction equation.

c. Explain why the standard error of b decreases as the sample size increases and when the x values display more variability.

a. Show that the smaller the value of s, the more precisely b estimates β.

b. Explain why a small s occurs when the data points show little variability about the prediction equation.

c. Explain why the standard error of b decreases as the sample size increases and when the x values display more variability.

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