# An agent for a residential real estate company in a large city would

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:

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 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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