ApartmentsThe following data represent the square footage

QUESTION:

Apartments  The following data represent the square footage and rents for apartments in Queens, New York.

(a) What are the estimates of \(\beta_0\) and \(\beta_1\)? What is the mean rent of a 900-square-foot apartment in Queens?

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

(c) Determine whether the residuals are normally distributed.

(d) If the residuals are normally distributed, determine \(s_{b_1}\).

(e) If the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, x, and response variable, y, at the \(\alpha = 0.05\) level of significance.

(f) If the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.

(g) Construct a 90% confidence interval for the mean rent of all 900-square-foot apartments in Queens.

(h) Predict the rent of a particular 900-square-foot apartment in Queens.

(i) Construct a 90% prediction interval for the rent of a particular 900-square-foot apartment in Queens.

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