An agent for a residential real estate company in a large city would like to be able to predict the...

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An agent for a residential real estate company in a large city would like to be able to predict the weekly rental cost for apartments based on the size of the apartment as defined by the number of square metres in area. A sample of 25 apartments was selected from across the city, and the information gathered recorded in the following table:

Apartment

Weekly Rent ($)

Size (square metres)

Apartment

Weekly Rent ($)

Size (square metres)

1

219

79

14

415

127

2

369

135

15

323

109

3

277

101

16

335

114

4

346

114

17

254

116

5

219

67

18

392

117

6

392

138

19

277

107

7

381

106

20

265

83

8

216

67

21

369

126

9

202

65

22

381

97

10

265

89

23

277

70

11

323

102

24

185

93

12

381

119

25

404

111

13

531

184

   

(a) What are the dependent and independent variables in this problem? Explain.

(b) Use the least-squares method to find the regression coefficients (show workings). State the simple linear regression equation.

(c) Interpret the meaning of both regression coefficients in this problem.
(d) Predict the weekly rental cost for an apartment that has an area of 100 square metres.

(e) Would it be appropriate to use the model to predict the weekly rental for an apartment that has an area of 50 square metres? Explain.

(f) Your friends are considering signing a lease for an apartment in this city. They are trying to decide between two apartments, one with an area of 100 square metres for a weekly rent of $294 and the other with an area of 120 square metres for a weekly rent of $329. What would you recommend to them? Why?

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