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Best Predictor of Winning Percentage, Take 2. Just scoring a lot of runs doesn't seem to be much of a predictor so let's use the LinRegTTest to probe a little deeper. Using the data below perform the same test for Runs Allowed vs. Winning Percentage . Run Differential (Runs Scored - Runs Allowed) vs. Winning Percentage Fill in the table below with your results (include Runs Scored results from the previous page) and determine which of the three relationships is the strongest. SD Phil Atl SF Chic Flor LAD Wash Ariz | NYM | Hou Runs Scored 665 772 738 697 685 719 667 655 713 656 611 Runs Allowed 581 640 629 583 767 717 692 742 836 652 729 Winning Pct. .556 .599 .562 .568 .463 494 494 .426 .401 .488 469 Coefficient of Correlation Determination P-Value (r) (r2) (p) Runs Scored VS. Winning Percentage Runs Allowed VS. Winning Percentage Run Differential VS. Winning Percentage Which one of these is the strongest predictor of winning percentage? A quick review: What is the strongest (value) that a correlation coefficient can be? One last question: What is a residual? WS CorReg.docx 2 of 2Best Predictor of Winning Percentage. Baseball analysts are constantly trying to find a key number that will predict winning percentage for games played. Below are the runs scored, runs allowed, and winning percentages for several teams in the National League 2010 season. SD Phil Atl SF Chic Flor |LAD Wash Ariz NYM Hou Runs Scored 565 772 738 697 685 719 667 655 713 656 611 Runs Allowed 581 640 629 583 767 717 692 742 836 652 729 Winning Pct. .556 .599 .562 .568 .463 .494 .494 426 .401 488 469 a. Calculate the correlation coefficient for this dataset comparing runs scored with winning percentage and show your work below. Round the answer to 3 decimal places. b. What percentage of the variation in winning percentage is explained by its linear relationship with runs scored? Show your work below. Show below C. Create a regression equation representing the relationship between runs question scored and winning percentage. Round answer values to 2 significant figures. d. Is there significant correlation between runs scored and winning percentage in this data? Show why or why not below. e. Based on the relationship between runs scored and winning percentage, what corresponding winning percentage would you predict for a team that scores 700 runs? Round the answer to 3 decimal places. f. Assuming a valid regression equation, outside what range should you not use the regression equation for predicting winning percentage with this dataset? g. In this problem what is the explanatory variable? (Hint: the answer is a word or words, not a variable name like x or y). WS CorReg.docx 1 of 2