An analyst at a credit card bank is looking at the relationship between customer

Question

An analyst at a credit card bank is looking at the relationship between customers' charges to the bank's card in two successive months. He selects 20 random customers, regresses charges in March(s) on charges in February (s), and finds an R^2 of 90%. He concludes that the model is a useful one for predicting one month's charges from the other. Examine the accompanying data and comment his conclusions Select the correct choice below and fill boxes to complete your choice. A. The analyst's conclusion is only somewhat correct The linear model can be used, but only to predict March charges using February charges B. There are two outliers that inflate R^2. Without those two points, R^2 drops from 90% to The analyst should set aside those two customers and refit the model (Round to the nearest integer as needed) C. The analysts conclusion is correct. D. There are two outliers that decrease R^2. Without those two points, R^2 increases from 90% to The analyst should set aside those two customers and use the new model. (Round to the nearest integer as needed)

Explanation / Answer

The statistical summary output without the outliers is:

Simple linear regression results:
Dependent Variable: Mar
Independent Variable: Feb
Mar = 1355.335 + 0.20797449 Feb
Sample size: 18
R (correlation coefficient) = 0.18138716
R-sq = 0.032901303
Estimate of error standard deviation: 2362.203

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Option B is correct.

There are two ouliers tthat inflates R2. Without these two points, R2 drops from 90% to 3%

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1355.335 684.04966 0 16 1.9813401 0.065 Slope 0.20797449 0.28188952 0 16 0.73778725 0.4713

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