Continuing Exercise 7, use the Distance, Weather, Wind15, Temperature, Grass, Pressure, and Ice explanatory variables as linear terms in a new logistic regression model and complete the following:

(a) Estimate the model and properly define the indicator variables used within it.

(b) The authors use "Sun" as the base level category for Weather, which is not the default level that R uses. Describe how "Sun" can be specified as the base level in R.

(c) Perform LRTs for all explanatory variables to evaluate their importance within the model. Discuss the results.

(d) Estimate an appropriate odds ratio for distance, and compute the corresponding confidence interval. Interpret the odds ratio.

(e) Estimate all six possible odds ratios for Weather, and compute the corresponding confidence intervals. Interpret the odds ratios. Is a value of 1 found to be within any of the intervals? Relate this result to the LRT performed earlier for Weather.

(f) Continuing part

(e), discuss how the overall family wise error rate could be controlled for all of the confidence intervals. Carry out the necessary computations.

(g) The purpose of this part is for you to estimate the probability of success for a field goal attempted by the Dallas Cowboys on December 12, 2011, in their game against the Arizona Cardinals. With the score tied and seven seconds remaining, the Dallas placekicker, Dan Bailey, attempted a 49-yard field goal that was successful. Unfortunately for Bailey, his coach, Jason Garrett, called a time out right before the attempt, so Bailey had to re-kick. Bailey was not successful the second time, so Garrett essentially "iced" his own kicker, and the Cardinals went on to win the game in overtime.28

i. Discuss the appropriateness of using the model here to estimate the probability success.

ii. The explanatory variable values for this placekick are: Distance = 49 yards, Wind15 = 0 (5 miles per hour), Grass = 1, Pressure = "Y", and Ice = 1. The game was played in Arizona's retractable roof domed stadium, and information about whether or not the roof was open is unavailable. For this part, assume then Weather = "Sun" and Temperature = "Nice". Find the estimated probability of success for this field goal.

iii. Compute the corresponding confidence interval for the probability of success.

(h) Is there evidence to conclude that icing the kicker is a good strategy to follow?

Exercise 7

Exercise 17 of Chapter 1 examined data from Berry and Wood (2004) to determine if if an "icing the kicker" strategy implemented by the opposing team would reduce the probability of success for a field goal. Additional data collected for this investigation are included in the placekick.BW.csv file. Below are descriptions of the variables available in this file:

• GameNum: Identifies the year and game

• Kicker: Last name of kicker • Good: Response variable ("Y" = success, "N" = failure)

• Distance: Length in yards of the field goal

• Weather: Levels of "Clouds", "Inside", "SnowRain", and "Sun"

• Wind15: 1 if wind speed is ≥15 miles per hour and the placekick is outdoors, 0 otherwise.

• Temperature: Levels of "Nice" (40?F

• Grass: 1 if kicking on a grass field, 0 otherwise

• Pressure: "Y" if attempt is in the last 3 minutes of a game and a successful field goal causes a lead change, "N" otherwise

• Ice: 1 if Pressure = 1 and a time-out is called prior to the attempt, 0 otherwise

Notice that these variables are similar but not all are exactly the same as given for the placekicking data described in Section

2.2.1 (e.g., information was collected on field goals only, so there is no PAT variable). Using this new data set, complete the following:

(a) When using a formula argument value of Good ~ Distance in glm(), how do you know if R is modeling the probability of success or failure? Explain.

(b) Estimate the model from part (a), and plot it using the curve() function.

(c) Add to the plot in part (b) the logit() = 5.8121 - 0.1150distance model estimated in Section 2.2.1. Notice that the models are quite similar. Why is this desirable?

Exercise 17

Before a placekicker attempts a field goal in a pressure situation, an opposing team may call a time-out. The purpose of this time-out is to give the kicker more time to think about the attempt in the hopes that this extra time will cause him to become more nervous and lower his probability of success. This strategy is often referred to as "icing the kicker." Berry and Wood (2004) collected data from the 2002 and 2003 National Football League seasons to investigate whether or not the strategy actually lowers the probability of success when implemented. Table 1.7 contains the results from the 31-40 yard field goals during these seasons under pressure situations (attempt is in the last 3 minutes of a game and a successful field goal causes a lead change). Complete the following:

(a) Calculate the Wald and Agresti-Caffo confidence intervals for the difference in probabilities of success conditioning on the strategy. Interpret the intervals.

(b) Perform a score test, Pearson chi-square test, and LRT to test for the equality of the success probabilities.

(c) Estimate the relative risk and calculate the corresponding confidence interval for it. Interpret the results.

(d) Estimate the odds ratio and calculate the corresponding confidence interval for it. Interpret the results.

(e) Is there sufficient evidence to conclude that icing the kicker is a good strategy to follow? Explain.