The following data represent the height (inches) of boys

QUESTION:

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 \(\beta_0\) and \(\beta_1\). What is the mean height of a 7-year-old boy?

(b) Compute the standard error of the estimate, \(s_e\).

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

(d) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares 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.