Chapter 8, Problem 1E

Credit card spending An analysis of spending by a sample of credit card bank cardholders shows that spending by cardholders in January (Jan) is related to their spending in December (Dec):

The assumptions and conditions of the linear regression seemed to be satisfied and an analyst was about to predict January spending using the model

$\widehat{Jan}=\$612.07+0.403Dec.$

Another analyst worried that different types of cardholders might behave differently. She examined the spending patterns of the cardholders and placed them into five market Segments. When she plotted the data using different colors and symbols for the five different segments, she found the following:

Look at this plot carefully and discuss why she might be worried about the predictions from the model

$\widehat{Jan}=\$612.07+0.403Dec.$

To determine

Being worried to make a prediction from the model $\text{Jan}=\$612.07+0.403\text{Dec}\text{.}$, using a second scatterplot.

Explanation of Solution

Given info:

A scatterplot of spending for a sample of credit card bank cardholders in January and in December is given. The corresponding regression model to predict January spending from December spending is $\text{Jan}=\$612.07+0.403\text{Dec}\text{.}$

Another scatterplot of spending for a sample of credit card bank cardholders in January and that in December for five market segments is given.

Justification:

The conditions for a scatterplot that is well-fitted for the data is as follows:

• Straight enough condition: The relationship between y and x is straight enough to proceed with a linear regression model.
• Outlier condition: No outlier must be there which influences the fit of the least square line.
• Thickness condition: The spread of the data around the generally straight relationship seems to be consistent for all values of x.

The different segments are not scattered at random throughout the scatterplot.

Thus, the spread of the data is not consistent for all values of December and each segment may have a different relationship that might affect the accuracy of the model to predict.

The relationship between the spending of credit card bank cardholders in January and in December is not straight enough to proceed with a linear regression model.