# Scatter plot and Linear Regression Equation Analysis

13.5 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.

13.9 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)?

https://brainmass.com/statistics/scatter-plot/scatter-plot-and-linear-regression-equation-analysis-282529

#### Solution Summary

For the given data, scatter plot togather with the estimated regression eqation is obtained. Interpretation estimated egression coefficient are given and the estimated regression equation is used for prediction. Detailed calculations are provided in the Excel file.

Simple Linear Regression Analysis

One of the editors of a major automobile publication has collected data on 30 of the best-selling cars in the United States. The editor is particularly interested in the relationship between highway mileage and curb weight of the vehicles.

a. Develop a scatter plot for these data. Discuss what the plot implies about the relationship between two variables. Assume that you wish to predict highway mileage by using vehicle curb weight.

b. Compute the correlation coefficient for the two variables and test to determine whether there is a linear relationship between the curb weight and the highway mileages of automobiles.

c. (1) Compute the linear regression equation based on the sample data (2) Cadillac's 1999 Sedan DeVille weight approximately 4,012 pounds. Provide an estimate of the average highway mileage you would expect to obtain from this model

[See automobile information attached in solution.]

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