Concept explainers
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
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
Being worried to make a prediction from the model
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
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.
Want to see more full solutions like this?
Chapter 8 Solutions
Intro Stats
- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardLife Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage