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?

(f) Determine the coefficient of determination , r^2, and interpret its meaning.

(g) Determine the standard error of estimate.(syx)

(h) How useful do you think this regression model is for predicting the monthly rent?

(i) Can you think of other variables that might explain the variation in the monthly rent?

Answer #1

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An agent for a real estate company in a large city would
like to be able to predict the monthly rental cost for apartments,
based on the size of the apartment, as defined by square footage.
A sample of eight apartments in a neighborhood was selected, and
the information gathered revealed the data shown below. For these
data, the regression coefficients are b0= 328.6794 and
b1=0.8881. Complete parts (a) through (d).
Monthly Rent ($)
Size (Square Feet)
925
750
1,500
1,250...

An agent for a real estate company in a large city collected
data on the sizes (X in square feet) and monthly rents (Y in
dollars) of a sample of eight apartments in a neighborhood. The
data is shown below.
Monthly Rent ($)
Size (Square Feet)
925
800
1550
1300
800
900
1450
1200
1900
2000
925
650
1750
1350
1300
950
A) Use the least-square method to find the regression
coefficients b0 and b1
B) What do b0 and...

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yi = 279.7 + 0.906 xi
Monthly Rent ($)
900
1500
800
1,600
1,950
950
1,750
1,350
Size (Square Feet)
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1,300
1,050
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