# ?The following data represent the height (inches) of boys between the ages of 2 and 10 years. (a) Treating age as the explanatory variable, de

**Chapter 14, Problem 3**

#### (choose chapter or problem)

The following data represent the height (inches) of boys between the ages of 2 and 10 years.

(a) Treating age as the explanatory variable, determine the estimates of b0 and b1. What is the mean height of a 7-year-old boy?

(b) Compute the standard error of the estimate, se.

(c) Assuming the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, age, and response variable, height, at the = 0.05 level of significance.

(d) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true leastsquares regression line.

(e) Construct a 90% confidence interval for the mean height found in part (a).

(f) Predict the height of a 7-year-old boy.

(g) Construct a 90% prediction interval for the height found in part (f).

(h) Explain why the predicted heights found in parts (a) and (f) are the same, yet the intervals are different.

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