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## NYU Statistics Regression Equations Analysis & Yearly Purchases Worksheet

### Question Description

1.A bank that offers charge cards to customers studies the yearly purchase amount (in thousands of dollars) on the card as related to the age, income (in thousands of dollars), whether the and years of education of the cardholder. The other variables are self-explanatory. The original data set has information on 150 cardholders. Upon further examination of the data, you decide to remove the data for cardholder 129 because this is an older individual who has a high income from having saved early in life and having invested successfully. This cardholder travels extensively and frequently uses her/his charge card. The data file New Purchases is posted on NYU classes.

a.Fit the model to data and give the least squares equation to predict yearly purchase amount.

b.Give practical interpretations of the estimates.

c.Is there sufficient evidence ( at ? = .05) to say that education is a useful predictor of yearly purchase amount.

d.Evaluate the overall utility of the model at ? =.01.

e.Find the 95% prediction interval for yearly purchase amount for 44 year old person with 20 years education and \$70,000 income.

2.The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output (with some values missing) was recently presented to the editors by the magazines analysts:

Regression Analysis: mileage, highway versus Curb Weight, cylinders, …

The regression equation is

mileage, highway = 49.2 – 0.00518 Curb Weight – 0.913 cylinders

+ _ _ _ Horse Power – 0.000102 Price as Tested

Predictor Coef SE Coef T P

Constant 49.173 3.220 15.27 0.000

Curb Weight -0.005180 0.001199 -4.32 0.000

cylinders -0.9132 0.7510 _ _ _

Horse Power _ _ _ _ 0.01676 0.89 0.384

Price as Tested -0.00010196 0.00004091 -2.49 0.020

S = _ _ _ _ _ R-Sq = _ _ _ R-Sq(adj) = _ _ _

Analysis of Variance

Source DF SS MS F

Regression _ _ 371.599 _ _ _ _ _ _

Residual Error __ _ _ _ _ _ _ _

Total _ _ 506.167

Curb mileage,

Obs Weight highway Fit SE Fit Residual St Resid

17 3560 21.000 25.484 0.728 -4.484 -2.04R

18 3240 24.000 28.863 0.873 -4.863 -2.26R

R denotes an observation with a large standardized residual.

Correlations: Curb Weight, cylinders, Horse Power, Price as Tested

Curb Weight cylinders Horse Power

cylinders 0.596

0.001

Horse Power 0.293 0.840

0.116 0.000

Price as Tested -0.030 0.457 0.766

0.877 0.011 0.000

Cell Contents: Pearson correlation

P-Value

Based on this output and your understanding of multiple regression analysis:

a)State the multiple regression equation and fill in the missing values.

b)Interpret the meaning of the regression coefficients for Curb Weight, and Horse Power in this problem.

c) Test to determine if this model is useful in predicting the highway miles per gallon (Y), use 0.01 level of significance.

d)At 0.01 level of significance, determine whether each explanatory variable make a significant contribution to the model?

e) What, if any, multicollinearity do you detect? Explain.

3.An auditor for a county government would like to develop a model to predict the county taxes based on the age of single-family houses. A random sample of 17 single-family houses bas been selected, with the following results:

Taxes Age

925 1

870 2

809 4

720 4

694 5

630 8

562 10

546 12

523 15

480 20

486 22

462 25

441 25

426 30

368 35

350 40

322 50

a) Set up a scatter diagram between age and county taxes.

b) State the liner regression equation.

c) State the quadratic regression equation. Determine whether there is a significant overall relationship between age and county taxes at the 0.05 level of significance.

d) Determine which one of the models is better to be used for predicting the average county taxes for a house. Use significant level 0.025.

e) Using the quadratic regression equation Predict the average county taxes for a house that is 20 years old.

4. In an effort to predict the price of a used BMW that will be sold to a car dealer at a local auction, a sample of 52 cars that were sold at auction recently was collected. (optional)

The data is in the file called BMW2 which is posted on NYU Classes provides the price (\$1000), odometer (miles), and series (different models 3, 5 or 7 series).

1. Develop three models:

1.Using only price and odometer to predict the price of the used BMW.

2.Using price, odometer, and series to predict the price of the used BMW.

3. Using price, odometer, series, and interaction terms to predict the price of the used BMW.

b.Test to determine if each model is useful in predicting the price of the used BMW.

c.Use the appropriate test to determine the best model.

Use the best model you have selected in part C to estimate the price of a 5 Series with 25,000 Miles

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