The following data represent the square footage and rents for apartments in Queens, New York and Nassau County, New York. For this problem, only consider the Queens data.

(a) What are the estimates of b0 and b1? What is the mean rent of a 900-square-foot apartment in Queens?
(b) Compute the standard error of the estimate, se.
(c) Determine whether the residuals are normally distributed.
(d) Determine sb1.
(e) If the residuals are normally distributed, test whether a linear relation exists between the explanatory variable, x, and response variable, y, at the a = 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.

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Nassau County (Long Island) Queens (New York City) Square Footage, x Rent per Month, y Rent per Month, y Square Footage, x 1875 500 650 1100 1075 588 1215 588 1000 2000 1250 1775 688 1655 556 1050 825 1250 825 1300 1259 2700 743 1475 $50 1200 660 1315 1400 560 1250 975 1073 2350 1429 1900 3300 1650 1452 800 1077 1305 3100 1395