Click Here for Helpful Hints

Regression analysis is often used in medical research to examine the variables that affect various biological processes. A study performed by psychology majors investigated nutritional effects on preweaning mouse pups. In the experiment, the amount of nutrients was varied by rearing the pups in different litter sizes. After 32 days, the body weight and brain weight (both measured in grams) were recorded. These data are stored in file (column 1 = brain weight; column 2 = litter size; column 3 = body weight).

        a. Conduct a multiple regression analysis where the dependent variable is the brain weight. Interpret the coefficients.
        b. Can we infer at the 5% significance level that there is a linear relationship between litter size and brain weight?
        c. Can we infer at the 5% significance level that there is a linear relationship between body weight and brain weight?
        d. What is the coefficient of determination, and what does it tell you about this model?
        e. Test the overall validity of the model. (Use a 5% significance level.)
        f.  Predict with 95% confidence the brain weight of a mouse pup that came from a litter of 10 pups and whose body weight is 8 grams.
        g. Estimate with 95% confidence the mean weight of all mouse pups that came from litters of 6 pups and whose body weight is 7 grams.

Source: D. E. Matthews and V. T. Farewell, Using and Understanding Medical Statistics (Karger, 1988).

The administrator of the school board in a Palm Beach County was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, she attempted to determine the factors that account for the differences. Accordingly, she took a random sample of 40 schools across the county and, for each, determined the mean test score last year, the percentage of teachers in each school who have at least one university degree in mathematics, the mean age, and the mean annual income of the mathematics teachers. These data are stored in columns 1 to 4, respectively, of file .

        a. Conduct a regression analysis to develop the equation.
        b. Is the model valid in explaining the variation among schools? Explain.
        c. Interpret and test the coefficients (with α = .05).
        d. Predict with 95% confidence the test score at a school where 50% of the mathematics teachers have mathematics degrees, the mean age is 43, and the mean annual income is $48,300 (if using full model).

Remember to right click the mouse to save!

University students often complain that universities reward professors for research but not for teaching, and argue that professors react to this situation by devoting more time and energy to the publication of their findings and less time and energy to classroom activities.  Professors counter that research and teaching go hand in hand; more research makes better teachers. A student organization at Florida Atlantic University decided to investigate the issue. They randomly select 250 professors employed by FAU. The students recorded the salaries of the professors, their average teaching evaluations (on a 10-point scale), the total number of journal articles published in their careers, and their years of service. These data are stored in columns 1 to 4, respectively, in file Perform a complete analysis (produce the regression equation, assess it, and diagnose it) and report your findings. 

Lotteries have become important sources of revenue for governments. Many people have criticized lotteries, however, referring to  them as a tax on the poor and uneducated. In an examination of the issue, a random sample of 100 adults was asked how much they spend on lottery tickets and was interviewed about various socioeconomic variables. The purpose of this study is to test the following beliefs.
        1 - Relatively uneducated people spend more on lotteries than do relatively educated people.
        2 - Older people buy more lottery tickets than younger people.
        3 - People with more children spend more on lotteries than people with fewer children.
        4 - Relatively poor people spend a greater proportion of their income on lotteries than relatively rich people.

The following data were stored in columns 1 to 5, respectively, of file .

        --Amount spent on lottery tickets as a percentage of total household income
        --Number of years of education
        --Age
        --Number of children
        --Personal income (in thousands of dollars)

                            a.  Develop the multiple regression equation.
                            b.  Is the complete model valid?
                            c. Test each of the beliefs at the 5% significance level.  What conclusions can you draw?

Click Here for Helpful Hints

©2008 David M. Compton, Ph.D.