A bank that offers charge cards to customers studies the yearly purchase amount

Question

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 160 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 “Purchases” is posted on Blackboard.

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.

Explanation / Answer

Solution:

a) The regression equation is
Purchase = -0.894 + 0.0259 Age + 0.0200 Income + 0.00985 Education
b) If age, income, and Education are equal to zero the yearly purchase is -0.894 unit or -$894.
  
If all the income and education held constant for one year increase in age the yearly purchase will increase by 0.0259 units or $25.90.

If all the age and Education held constant for $1000 increase in income in income the yearly purchase will increases by $20.00
If all age and income held constant for one year increase in education the yearly purchase will increases by $9.85.

c) P-value = 0.005 < = 0.01 reject Ho, education is a useful predictor of yearly purchase amount.

d) Since P-value = 0.00 < = 0.01 reject the model is useful.
e) (1.65011, 2.03460)

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