Size (Square feet) Rent ($) 524 1110 616 1175 666 1190 830 1410 450 1210 550 1225 780 1480 815 1490 1070 1495 610 1680 835 1810 660 1625 590 1469 675 1395 744 1150 820 1140 912 1220 628 1434 645 1519 840 1105 800 1130 804 1250 950 1449 800 1168 787 1224 960 1391 750 1145 690 1093 840 1353 850 1530 965 1650 1060 1740 665 1235 775 1550 960 1545 827 1583 655 1575 535 1310 625 1195 749 1200 634 1185 641 1444 860 1385 740 1275 593 880 895 692 1050 1650 1340 1560 Size (Square feet) Rent ($) 524 1110 616 1175 666 1190 830 1410 450 1210 550 1225 780 1480 815 1490 1070 1495 610 1680 835 1810 660 1625 590 1469 675 1395 744 1150 820 1140 912 1220 628 1434 645 1519 840 1105 800 1130 804 1250 950 1449 800 1168 787 1224 960 1391 750 1145 690 1093 840 1353 850 1530 965 1650 1060 1740 665 1235 775 1550 960 1545 827 1583 655 1575 535 1310 625 1195 749 1200 634 1185 641 1444 860 1385 740 1275 593 1050 880 1650 895 1340 692 1560 a. Construct a scatter plot. Solution Done b. Use the least-squares method to determine the regression coefficients b0 and b1. Solution: The estimate of bo is 992.99 and b1 is 0.49 c. Interpret the meaning of b0 and b1 in this problem. Solution: b0 represents the intercept and tell the average value of dependent variable when all the indpendent variable are zero b1 represent the slope of the regression line and provide the change in dependent variable with a unit change in the independent variable. d. Predict the mean monthly rent for an apartment that has 800 square feet. Solution: The Regression line equation would be: Rent = 992.99 +0.49xSize when Size is 800 Square feet, the Rent would be: = 992.99 + 0.49x800 = 1384.99 ~ $1385 e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 1,500 square feet? f. Your friends Jim and Jennifer are considering signing a lease for a one-bedroom apartment in this residential neighborhood. They are trying to decide between two apartments, one with 800 square feet for a monthly rent of $1,130 and the other with 830 square feet for a monthly rent of $1,410. Based on (a) through (d), which apartment do you think is a better deal? SUMMARY OUTPUT Regression Statistics Multiple R 0.35 R Square 0.13 Adjusted R Square 0.11 Standard Error 186.04 Observations 48.00 ANOVA df Regression Residual Total Intercept Size (Square feet) 1.00 46.00 47.00 SS 228565.19 1592111.79 1820676.98 Coefficients 992.99 0.49 Standard Error 147.37 0.19 MS 228565.19 34611.13 t Stat 6.74 2.57 F Significance F 6.60 0.01 P-value 0.00 0.01 Lower 95% Upper 95% 696.36 1289.63 0.11 0.88 Scatter plot of Size and Rent 2000 1800 1600 1400 1200 Rent ($) 1000 800 600 400 200 0 400 500 600 700 800 Size (Square Foot) 900 1000 1100 1200