(a) Construct a scatter plot. (b) Use the least-squares method to determine the regression coefficients (intercept and slope). (c) Interpret the meaning of the intercept and slope in this problem. (d) Predict the monthly rent for an apartment that has 1000 square feet. (e) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?

Question

An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

 

 

Size (square feet)

Rent ($)

850

1950

1450

2600

1085

2200

1232

2500

718

1950

1485

2700

1136

2650

726

1935

700

1875

956

2150

1100

2400

1285

2650

1985

3300

1369

2800

1175

2400

1225

2450

1245

2100

1259

2700

1150

2200

896

2150

1361

2600

1040

2650

755

2200

1000

1800

1200

2750

 

 

(a) Construct a scatter plot.

(b) Use the least-squares method to determine the regression coefficients (intercept and slope).

(c) Interpret the meaning of the intercept and slope in this problem.

(d) Predict the monthly rent for an apartment that has 1000 square feet.

(e) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?

 

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