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?

ONLY ANSWER THIS QUESTION IF YOU CAN ANSWER IT COMPLETELY A THROUGH I AND LABEL YOUR ANSWERS!!!

Answer 1

Answer:

a)

b)

c)

y = 1177.12 + 1.065 * x

Interpretation:

Intercept: 1177.12

Intercept is the expected mean value of Y when X = 0 i.e., if x = 0, then predicted value is equal to the intercept

Slope: 1.065

If the value of x is increased by 1 unit then the predicted value will increase by 1.065 units

d)

for, x = 1000 square feet,

Predicted monthly rent = 1177.12 + 1.065 * 1000 = $2242.12