Analysis of Variance ANOVA Regression and Correlation

1. Annual bonuses ($1,000) of six randomly selected employees and their years of service were recorded
and listed below.
A. Perform a linear regression analysis to determine the equation, model validity, relation coefficient of
the independent variable, t-value, and p-value of the independent variable and interpret the results.
B. Perform a correlation analysis to determine the correlation coefficient and coefficient of
determination and interpret the results.
Years (x) 1 2 3 4 5 6
Bonuses (y) 6 1 9 5 17 12
2. Life insurance companies are very interested in predicting how long their client will live because their
premiums and profitability depend on this variable. An actuary for an individual insurance company
gathered data from 100 recently deceased male clients. Recorded the age of death of the client, the

3/7/23, 4:33 PM Module 6 Assignment: Analysis of Variance (ANOVA), Regression and Correlation
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– Official Assignment Rubric
ages at the death of his mother and father, the ages at the death of his grandmother and grandfather,
and the smoking or non-smoking habit of the client. (Xr18-10 Module 6

A. Perform a regression analysis of this data.
B. Comment on the validity of the regression model.
C. Determine which independent variables had a linear relationship with customer longevity at 95%
confidence.
D. Interpret each coefficient of the regression.
E. Predict with 95% a level of confidence that the longevity of a man whose parents lived 70 years, his
grandmother lived 80 years, his grandfather lived 75 and is not a smoker.
3. A manufacturer of outdoor copper mailboxes and lamps has received numerous complaints about
premature corrosion. The manufacturer has identified the cause of the problem as the low-quality
varnish used to coat the copper. The manufacturer decides to replace the current varnish supplier with
one of five possible alternatives. To determine which is best, use each of the five varnishes to coat 25
copper mailboxes and place the 125 mailboxes outside. Records, for each, the number of days until
the first sign of corrosion is observed. (Xr15-12 Module 6

A. State the null and alternate hypothesis for this scenario.
B. Is there enough evidence at the significance level of 5% to allow the manufacturer to conclude that
there are differences between the five varnishes?
C. What are the conditions required for the test performed in part b? Explain?
D. Does it appear that the required conditions of the test in part b are met? Explain?