Apartment Size (sq feet) Rent ($) 1 521 1103 2 606 1189 3 666 1179 4 836 1414 5

Question

Apartment Size (sq feet) Rent ($) 1 521 1103 2 606 1189 3 666 1179 4 836 1414 5 449 1214 6 549 1231 7 796 1490 8 803 1473 9 1085 1511 10 600 1679 11 827 1814 12 666 1644 13 583 1487 14 688 1378 15 753 1156 16 826 1139 17 927 1219 18 636 1431 19 656 1508 20 852 1096 21 804 1139 22 800 1262 23 933 1457 24 812 1168 25 787 1218 26 944 1383 27 739 1146 28 683 1095 29 854 1352 30 837 1527 An agent for a real estate company in a suburb has the business objective of developing more accurate estimates of the monthly rental cost for apartments. The agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent collects data from a sample of 30 one-bedroom apartments. Complete parts (a) through (c). a. Construct a 90% confidence interval estimate of the mean monthly rental for all one-bedroom apartments that are 794 square feet in size. 1281.33 lessthanorequalto mu_Y|X = 794 lessthanorequalto 1408.35 b. Construct a 90% prediction interval of the monthly rental for an individual one-bedroom apartment that is 794 square feet in size. lessthanorequalto Y_X = 794 lessthanorequalto (Type integers or decimals. Round to two decimal places as needed. Use ascending order.)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Rent ($)
Independent Variable: Size (sq feet)
Rent ($) = 1196.485 + 0.18684837 Size (sq feet)
Sample size: 30
R (correlation coefficient) = 0.13617406
R-sq = 0.018543375
Estimate of error standard deviation: 195.15163

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

90% prediction interval will be:

1006.84 < Y < 1682.84

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1196.485 196.08769 0 28 6.101785 <0.0001 Slope 0.18684837 0.25689252 0 28 0.72734063 0.4731

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