STA 431 Assignment Six:

Quiz in Tutorial on Friday Feb. 18th

In the United States, admission to university is based partly on high school marks and recommendations, and partly on applicants' performance on a standardized multiple choice test called the Scholastic Aptitude Test (SAT). The SAT has two sub-tests, Verbal and Math. A university administrator selects a random sample of 200 applicants, and obtains the Verbal SAT, the Math SAT and first-year university Grade Point Average (GPA) for each student. She wants an equation for predicting GPA from Verbal SAT and Math SAT. That is, predicted GPA will be a function of two variables, Verbal SAT and Math SAT. The raw data are available in the file sat.data. Note that the course website now has a data sets link, and you can also reach the data from there.

Write a SAS program and produce output that will allow you to answer questions such as the following from your printout. Bring printouts of your log file and list file to the quiz. You may be asked to hand them in, and you will need them to answer the quiz questions. You should also bring a calculator to the quiz.

Be ready to answer questions like the following:

• What is the mean Verbal SAT score?
• What is the standard deviation of the GPAs?
• What is the maximum likelihood estimate of β₁? The answer is a number.
• Write down the prediction equation based on material in your list file. Denote predicted GPA by Y-hat, Verbal SAT by X₁ and Math SAT by X₂. All other components of the formula should be numbers.
• What GPA would be predicted for a student with a verbal SAT of 600 and a math SAT of 650? Your answer is a number.
• What proportion of the sample variation in GPA is explained by the two components of the SAT test? The answer to this question is a single number between zero and one. (It's R².)