Discuss the below:
Scatter plot and Linear Regression Equation Analysis
Q1: Circulation is the lifeblood of the publishing business. The larger the sales of a magazine, the more it can charge advertisers. Recently, a circulation gap has appeared between the publishers reports of magazines newsstand sales and subsequent audits by the Audit Bureau of Circulations. The data below represent the reported and audited newsstand sales ( in thousands) in 2001 for the following 10 magazines:
Magazine Reported (X) Audited (Y)
YM 621.0 299.6
CosmoGirl 359.7 207.7
Rosie 530.0 325.0
Playboy 492.1 336.3
Esquire 70.5 48.6
TeenPeople 567.0 400.3
More 125.5 91.2
Spin 50.6 39.1
Vogue 353.3 268.6
Elle 263.6 214.3
A. Construct a scatter plot
B. Interpret the meaning of the slope, b in this position
C. Predict the mean audited newsstand sales for a magazine that reports the newsstand sales of 400,000.
Q2: An agent for a residential 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 the square footage. A sample of 25 apartments in a particular residential neighborhood was selected, and the information gathered revealed the following:
Rent($) Size(SquareFeet)
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
A. Construct a scatter plot.
B. Use the least squares method to find the regression coefficients b(0) and b(1).
C. Interpret the meaning of b(0) and b(1) in this problem.
D. Predict the mean monthly rent for an apartment that has 1,000 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. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and with the other 1,200 square feet for a monthly rent of $1,425. What would you recommend to the based on (a) through (d)?