Exercises
(1) BIGTEN.SAV: Graduation Rates at Big Ten Universities (Source: Berk,
1994, p. 82, modified).
One of the factors thought to determine graduation rates at universities is the motivation and scholastic aptitude of its
students. To test this theory, a researcher collects data on graduation rates (UPERCENT: percentage of students
graduating within 5 years of entry) and the average ACT scores of incoming freshman (variable ACT). Data are:
UPERCENT ACT
76.2 27
57.6 24
55.4 24
59.7 23
86.0 28
46.2 22
66.7 23
(A) Enter this data set into a file and then create a scatter plot of the data. Narratively describe the relationship
between ACT and UPERCENT.
(B) Calculate and interpret r.
(C) Regress ACT on UPERCENT and determine the regression equation. Use this regression equation to predict the
graduation rate of a school with an average ACT score of 25.
(D) Test the regression coefficient for significance. (List the null and alternative, let a = .05, etc.)
(E) Summarize in narrative form, your findings.
(2) IGUANA: Iguana Eggs Over Easy (Source: Hampton, 1994, p. 157,
modified).
We want to determine the relationship between female iguana body weight and the number of eggs they produce. Data
from a random sample of 9 gravid iguanas are:
ID Weight Eggs
--- ------ ------
1 0.90 33
2 1.55 50
3 1.30 46
4 1.00 33
5 1.55 53
6 1.80 57
7 1.50 44
8 1.05 31
9 1.70 60
(A) Create a data file with these data.
(B) Produce a scatter plot and describe the relationship you see narratively.
(C) Compute the regression coefficients and write the regression equation used to predict the average number of
iguana eggs based on body weight. Use this equation to predict the average number of eggs produced by a 1 kilogram
Iguana.
(D) Test the model's slope for significance. Let a = .01. List all hypothesis testing steps (e.g., Null and alterative, etc.)
(E) Compute the correlation coefficient. Interpret these results.
(3) FEV.SAV: Forced expiratory volume survey.
If you don't already have it, download the file FEV.SAV. We wish to describe the relationshiup between AGE (years)
and HEIGHT (inches).
(A) Produce a scatter plot and describe what you see.
(B) Determine the regression model for these data, and predict the average height of a 10-year old.
(C) Test the model's slope for significance. Let alpha = .01. (Perform all hypothesis testing steps, from listing the null
and alterative hypotheses, to formulating the conclusion.)
(D) Compute the correlation coefficient and describe (in words) the correlation between body weight and egg
production.
(4) ALCOHOL.SAV: Alcohol Consumption Survey (Data: Monder, 1986)
We want to study the relationship between alcohol consumption score (ALCS) and AGE using correlation and
regression techniques. ALCS is an ordinal variable that indexes the number of alcoholic beverages consumed on a
weekly basis. .
(A) Determine the correlation coefficient between these two factors, and test it for significance.
(B) Perform a regression analysis. Using an alpha level of .05, test the significance of the regression model. Identify
the null and alternative hypotheses.
(C) Predict the average alcohol consumption score of a typical 40-year-old.