Question 1.

The Olympic Selection Committee is interested in the variables that impact the overall success of 2016 Summer Olympics in Rio. Examine the Venn Diagram on the last page of this exam very carefully. (This is supposed to look like the Olympic symbol). Use the letters corresponding to each part of this diagram to answer the following questions.

1a. Which part(s) represent the following bivariate (zero-order) relationships? between X2 and Y?
between X4 and Y?

between X3 and X4?

1b. Which part(s) represent the following partial correlations? (4 points) between X3 and Y, controlling for X2
between X1 and Y, controlling for all other variables.

1c. In examining the partial correlation between X 2 and Y, which part(s) would be partialled out (removed):

From X2 From Y

1d. Represent the semi-partial correlation between X4 and Y, controlling for the influence of X3.

Numerator (part) =

denominator (whole) =

1e. Which part represents the unique contribution (semi-partial correlation) of X2 toward the explanation of the variance in Y? (2 pts)

1f. In order to test the significance of the semi-partial correlation identified in 1e above, an R2 Change is computed and tested using the F change test..

Which parts define the biggest R2 ? Use all IVs.

Which parts define the R2 which will be removed (subtracted) to arrive at the part representing the unique contribution of X2 ?

Question 2

Results from a research study are summarized below. The researcher was interested in the effects of a new drug in reducing cholesterol. She randomly assigned 50 participants to two groups. The first group received the new drug while the second group received a placebo. The researcher believed that the amount of time each person spent exercising might confound the effects of this drug so each person was asked to report this information.

The following results were obtained.

The R2 between the dependent variable (cholesterol) and exercise was computed to be .50. The R2 between the dependent variable and the treatment (drug vs. placebo) was found to .60 The R2 between the dependent variable and both treatment and exercise was .75

Please answer the following questions regarding this research problem. Specifically, the researcher wants to know if the treatment (drug) has an impact on cholesterol levels, when controlling for the influence of exercise.

2a. What type of analysis is most appropriate for this situation

2b. Describe assumptions which should be examined before applying this analysis.

2c. Describe the specific steps (NOT in SPSS terms) you would take to investigate this problem. Be specific and be sure to use the information summarized above in any calculations which are necessary to address the research problem. (7 pts) (you might want to use the reverse side or attach an additional sheet here)

2d. What can be concluded about the effects of the treatment on the cholesterol level of subjects? Use the information you analyzed from 3c.

Question # 3

A graduate assistant with the athletic department was studying data pertaining to the success of the Auburn football team in making field goals. If the probability of making a field goal could be predicted accurately when considering relevant variables, it would be very helpful in determining whether to attempt or not to attempt field goals at critical moments in the game. This graduate assistant began to analyze data from previous field goal attempts.

Specifically, the variables of distance in yards (YARDS), angle on the field (ANGLE), and windspeed (WINDSPD) were examined. Because the outcome is either success or failure on each field goal, a logistic regression was performed. Based on the results from this logistic regression (see attached pages), answer the following questions.

3a. Why is YARDS selected as the in the first step of this analysis?

3b. Examining the results from Section B of the results, interpret the Exp (B).
Specifically, what happens to the odds of making a field goal as YARDS increase by 1 yard?

3c. Examine the results in Section C of the output. What evidence from this section supports the addition of ANGLE to the model in Step 2?

3d. Continue to examine the results in Section D. Examine the results pertaining to variable NOT in the equation. Would the remaining variable (WINDSPD) be added in Step 3? Support your response with evidence from this section.

3e. Using the information reported in Section D, determine the prediction equation used to predict the log-odds of making a field goal.

3f. Briefly explain why log-odds are predicted using regression when what we are really interested in are probabilities.