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 ß₀ and ß₁. 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 α = 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.

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Boy Boy Boy Age, x Height, y Age, x Height, y Age, x Height, y 2 36.1 5 45.6 48.3 2 34.2 5 44.8 50.9 2 31.1 5 44.6 52.2 3 36.3 6 49.8 51.3 39.5 7 43.2 55.6 41.5 7 47.9 59.5 38.6 8 51.4 نیا 3 نیا 4 4 8 8 9 9 10 10