Question

American Express Company has long believed that its cardholders tend to travel more extensively than others-both on business and for pleasure. As part of a comprehensive research effort undertaken by a New York marketing research firm on behalf of American Express, a study was conducted to determine the relationship between miles traveled (x) and charges made on the American Express card (y). Eight cardholders were randomly selected and their total charges recorded for a specified period. A questionnaire was then mailed to these five cardholders requesting information on the number of miles traveled during this time period. The data follow.

Sick Days & Age

Cardholder Miles (1,000's) Charges ($1,000's) 1 1.2 2 2 2.0 3 3 1.5 2.3 4 2.3 2.3 5 1.7 2.3 6 0.5 2.7 7 2.1 2.1 8 0.8 3.4

A regression Analysis has been performed to estimate the model and the output is given.

Regression Statistics

Multiple R 0.40306 R Square 0.16246 Adjusted R Square 0.02287 Standard Error 0.47682 Observations 8

ANOVA

	df	SS	MS	F	Significance F
Regression	1	0.26460	0.26460	1.16380	0.32213
Residual	6	1.36415	0.22736
Total	7	1.62875

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.97185	0.45796	6.48933	0.00064	1.85126	4.09244
Miles	-0.30370	0.28152	-1.07879	0.32213	-0.99255	0.38515

Step 1 of 4:

What is the standard deviation of the error terms?

Step 2 of 4:

What fraction of the variation in credit card charges is explained by miles traveled?

Step 3 of 4:

What is the predicted value of credit card charges (in thousands of dollars) if the cardholder traveled 2 thousand miles?

Step 4 of 4:

Determine the 95% confidence interval for the average credit card charges, given that the cardholder traveled 2 thousand miles.

Answer 1