Question: The Colorado Rockies play their major league home baseball games in Coors Field, Denver. Each year, the Rockies are among the leaders in team batting statistics (e.g. home runs, batting average, and slugging percentage). Many baseball experts attribute this phenomenon to the “thin air” of Denver – called “The Mile-High City” due to its elevation. Chance (Winter 2006) investigated the effects of elevation on slugging percentage in Major League Baseball. Data was compiled on players’ composite slugging percentages at 11 of the 30 cities where Major League Baseball is played for the 2003 season, as well as on each of these 11 cities’ respective elevation (feet above sea level). The regression output is below. Please answer the questions that follow.

(a) Which variable is the dependent variable, y?

(b) Which variable is the independent variable, x?

(c) What is the value of the correlation coefficient, r. What does this tell you about the strength AND direction of the relationship?

(d) What is the value of the coefficient of determination, r2? What does this tell you?

(e) Is the overall model significant at the 5% level? Yes or No? How can you tell? What does this mean?

(f) What is the regression equation?

(g) What is the predicted slugging % if the elevation is 2,000 ft? Use the equation.

(h) What is the predicted elevation if the slugging % is 0.620? Use the equation.

(i) Only data for 11 of the 30 cities with MLB stadiums was collected. Denver, the “Mile-High City” is one of those data points. Please circle which one it is on the scatterplot and specifically explain why that point represents Denver.

(j) Overall, do you think this is a good model to use for the relationship between elevation and slugging %? Yes or No (only one is correct)? Mention 2 things in the output that supports your answer of yes or no.

(k) If you were a statistician, what 2 suggestions would you have for Major League Baseball, if they were interested in developing a more accurate regression equation about the relationship between elevation and slugging %?