Focusing on Data Analysis - UWEC Undergraduates

The file named Focus.txt in the Focus Database section of the WeissStats site contains information on the undergraduate students at the University of Wisconsin - Eau Claire (UWEC). Those students constitute the population of interest in the Focusing on Data Analysis sections that appear at the end of each chapter of the book.

Thirteen variables are considered. Table 1.9 lists the variables and the names used for those variables in the data files. We call the database of information for those variables the Focus database.

Also provided in the Focus Database section is a file called FocusSample.txt that contains data on the same 13 variables for a simple random sample of 200 of the undergraduate students at UWEC. Those 200 students constitute a sample that can be used for making statistical inferences in the Focusing on Data Analysis sections. We call this sample data the Focus sample.

Large data sets are almost always analyzed by computer, and that is how you should handle both the Focus database and the Focus sample. We have supplied the Focus database and Focus sample in several file formats in the Focus Database section of the WeissStats site.

If you use a statistical software package for which we have not supplied a Focus database file, you should (1) input the file Focus.txt into that software, (2) ensure that the variables are named as indicated in Table 1.9, and (3) save the worksheet to a file named Focus in the format suitable to your software, that is with the appropriate file extension. Then, any time that you want to analyze the Focus database, you can simply retrieve your Focus worksheet. These same remarks apply to the Focus sample as well as to the Focus database.

TABLE - 1.9 Variables and variable names for the Focus database

Recall from Chapter that the Focus database and Focus sample contain information on the undergraduate students at the University of Wisconsin - Eau Claire (UWEC). Now would be a good time for you to review the discussion about these data sets.

Open the Focus sample worksheet in the technology of your choice and do the following.

a. Find the linear correlation coefficient between cumulative GPA and high school percentile for the 200 UWEC undergraduate students in the Focus sample.

b. Repeat part (a) for cumulative GPA and each of ACT English score, ACT math score, and ACT composite score.

c. Among the variables high school percentile, ACT English score, ACT math score, and ACT composite score, identify the one that appears to be the best predictor of cumulative GPA. Explain your reasoning.

Now perform a regression analysis on cumulative GPA, using the predictor variable identified in part (c), as follows.

d. Obtain and interpret a scatter plot.

e. Find and interpret the regression equation.

f. Find and interpret the coefficient of determination.

g. Determine and interpret the three sums of squares SSR, SSE, and SST.