Question

4. An agent for a residential real estate company in a suburb located outside a major city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward the 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 8 one-bedroom apartments and the data are shown. Complete parts (a) through (f). Monthly Rent ($) 975 1,600 850 1,600 1,950 975 1,825 1,250 Size (Square Feet) 900 1,350 1,050 1,150 1,900 750 1,250 1,100 a. Construct a scatter plot. Choose the correct graph below. OB. Oc. O A. A Rent ($) 2,000+ A Rent ($) A Rent ($) 2,0007 2,000 2,000 7 Rent (5) 0 o+ 0 2,000 Size (Sq ft) 0 2,000 Size (sq ft) 2,000 of 2,000 2,000 Size (Sq ft) Size (Sq ft) b. Use the least-squares method to determine the regression coefficients bo and b. (Round to one decimal place as bo = needed.) b1 = (Round to one decimal place as needed.) c. Interpret the meaning of bo and b, in this problem. Choose the correct answer below. O A. For each increase of 1 square foot in space, the monthly rent is expected to increase by b, dollars. Since X cannot be zero, bo has no practical interpretation. O B. For each increase of 1 square foot in space, the monthly rent is expected to increase by bo dollars. Since X cannot be zero, b, has no practical interpretation. OC. For each increase of 1 square foot in space, the monthly rent is expected to increase by bo dollars. Apartments in this neighborhood cost at least by dollars. O D. For each increase of 1 square foot in space, the monthly rent is expected to increase by by dollars. Apartments in this neighborhood cost at least bo dollars. d. Predict the mean monthly rent for an apartment that has 1,000 square feet. The predicted mean monthly rent for such an apartment is $ (Round to the nearest cent as needed.)

Answer 1

a)

Ос. A Rent ($) 2,0007 2,000 Size (Sqft)

b)

(y-7) 900 1350 1050 1150 1900 750 1250 1100 9450 1181.250 975 1600 850 1600 1950 975 1825 (x-) 79101.5625 28476.5625 17226.5625 976.5625 516601.5625 185976.5625 4726.5625 6601.5625 839687.5000 SSX 162509.77 49228.52 278916.02 49228.52 327041.02 162509.77 199697.27 16416.02 1245546.88 SSY (x-x)(y-7) 113378.9063 37441.4063 69316.4063 -6933.5938 411035.1563 173847.6563 30722.6563 10410.1563 839218.7500 SXY 1250 Total Mean 11025 1378.13 sample size n= Spe Z(X--X)2 = EX--X)(y-7)= slope= B. = S/S intercepta Bo = V-B.X= 1378.1250 1181.2500 839687.500 839218.750 0.99944 197.53443

bo =197.5

b1=1.0

c)

O A. For each increase of 1 square foot in space, the monthly rent is expected to increase by by dollars. Since X cannot be zero, bo has no practical interpretation

d)

predicted val=197.5+1000*1=

1197

e)

O A. An apartment with 500 square feet is outside the relevant range for the independent variable.

f)

1200 is correct since its residual is smaller