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Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows: ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of errors. SO/IP: The average number of strikeouts per inning pitched. HR/IP: The average number of home runs per inning pitched. R/IP: The number of runs given up per inning pitched. The data in the Excel Online file below show values for these statistics for a random sample of 20 pitchers from the American League for a season. Construct a spreadsheet to answer the following questions.

Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows: ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of errors. SO/IP: The average number of strikeouts per inning pitched. HR/IP: The average number of home runs per inning pitched. R/IP: The number of runs given up per inning pitched. The data in the Excel Online file below show values for these statistics for a random sample of 20 pitchers from the American League for a season. Construct a spreadsheet to answer the following questions.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 87CR
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Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows:

  • ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of errors.
  • SO/IP: The average number of strikeouts per inning pitched.
  • HR/IP: The average number of home runs per inning pitched.
  • R/IP: The number of runs given up per inning pitched.

The data in the Excel Online file below show values for these statistics for a random sample of 20 pitchers from the American League for a season. Construct a spreadsheet to answer the following questions.

Excel template - Saved ✓ J2 File 123456789UIDE1 A Player Verlander, J Beckett, J Wilson, C Sabathia, C Haren, D McCarthy, B Santana, E Lester, J 10 Hernandez, F Buehrle, M 12 Pineda, M 13 Colon, B 14 Tomlin, J Pavano, C 16 Danks, J 17 Guthrie, J 18 19 20 Davis, W 21 22 23 24 25 26 27 28 29 30 31 32 33 34 25 Home 15 Lewis, C Scherzer, M Porcello, R Insert B Team DET BOS TEX NYY LAA OAK LAA BOS SEA CWS SEA NYY CLE MIN CWS BAL TEX DET TB DET Arial fx с W 24 H6969 13 16 19 16 11 15 14 13 9 8 12 9 8 9 14 15 11 14 Draw 5778 O 10 9 12 9 14 9 10 10 7327099 13 12 17 10 After reading these instructions delete all text in this shaded area. D I J H R/IP L 10 Page Layout ✓10 Data + Calculation Mode: Automatic Workbook Statistics E ERA B 2.40 2.89 2.94 2.99 3.17 3.32 3.37 3.46 3.46 3.59 3.74 3.99 4.24 4.30 4.33 4.32 4.39 4.42 4.44 4.75 F SO/IP Formulas 0.99 0.90 0.92 0.96 0.81 0.72 0.77 0.95 0.94 0.53 1.01 0.82 0.54 0.46 0.78 0.62 0.83 0.88 0.56 0.57 G HR/IP Search (Option 0.10 0.10 0.06 0.07 0.07 0.05 0.10 0.10 0.08 0.09 0.11 0.12 0.14 0.10 0.10 0.12 0.16 0.15 0.13 0.09 Data Review 0.28 0.34 0.40 0.37 0.38 0.43 0.42 0.39 0.41 0.44 0.43 0.51 0.48 0.55 0.51 0.53 0.51 0.51 0.52 0.57 + Q) View Help K General L ←.0 .00 M .00 →.0 N P After reading these instructions delete all text in this shaded area. Use the XLMiner Analysis ToolPak to conduct your Linear Regression analysis. After deleting all text in this shaded area, set the output range in the ToolPak to the top left cell of this area (J2). Your Linear Regression analysis output should fit into this shaded area. Editing Σ ✓ AY R Give Feedback to Microsoft Comments T S > 100% +
Transcribed Image Text:Excel template - Saved ✓ J2 File 123456789UIDE1 A Player Verlander, J Beckett, J Wilson, C Sabathia, C Haren, D McCarthy, B Santana, E Lester, J 10 Hernandez, F Buehrle, M 12 Pineda, M 13 Colon, B 14 Tomlin, J Pavano, C 16 Danks, J 17 Guthrie, J 18 19 20 Davis, W 21 22 23 24 25 26 27 28 29 30 31 32 33 34 25 Home 15 Lewis, C Scherzer, M Porcello, R Insert B Team DET BOS TEX NYY LAA OAK LAA BOS SEA CWS SEA NYY CLE MIN CWS BAL TEX DET TB DET Arial fx с W 24 H6969 13 16 19 16 11 15 14 13 9 8 12 9 8 9 14 15 11 14 Draw 5778 O 10 9 12 9 14 9 10 10 7327099 13 12 17 10 After reading these instructions delete all text in this shaded area. D I J H R/IP L 10 Page Layout ✓10 Data + Calculation Mode: Automatic Workbook Statistics E ERA B 2.40 2.89 2.94 2.99 3.17 3.32 3.37 3.46 3.46 3.59 3.74 3.99 4.24 4.30 4.33 4.32 4.39 4.42 4.44 4.75 F SO/IP Formulas 0.99 0.90 0.92 0.96 0.81 0.72 0.77 0.95 0.94 0.53 1.01 0.82 0.54 0.46 0.78 0.62 0.83 0.88 0.56 0.57 G HR/IP Search (Option 0.10 0.10 0.06 0.07 0.07 0.05 0.10 0.10 0.08 0.09 0.11 0.12 0.14 0.10 0.10 0.12 0.16 0.15 0.13 0.09 Data Review 0.28 0.34 0.40 0.37 0.38 0.43 0.42 0.39 0.41 0.44 0.43 0.51 0.48 0.55 0.51 0.53 0.51 0.51 0.52 0.57 + Q) View Help K General L ←.0 .00 M .00 →.0 N P After reading these instructions delete all text in this shaded area. Use the XLMiner Analysis ToolPak to conduct your Linear Regression analysis. After deleting all text in this shaded area, set the output range in the ToolPak to the top left cell of this area (J2). Your Linear Regression analysis output should fit into this shaded area. Editing Σ ✓ AY R Give Feedback to Microsoft Comments T S > 100% +
X Open spreadsheet Complete the equation below for an estimated regression equation developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP) (to 3 decimals). R/IP = SO/IP + HR/IP a. Use the F test to determine the overall significance of the relationship. Compute F test statistic (to 2 decimals). The p-value is (to 3 decimals). What is your conclusion at the .05 level of significance? a significant overall relationship. b. Use the t test to determine the significance of each independent variable. Compute the t test statistic for the significance of SO/IP (to 2 decimals). There is + The p-value is (to 3 decimals). What is your conclusion at the .05 level of significance? significant. SO/IP is The p-value is î Compute the t test statistic for the significance of HR/IP (to 2 decimals). (to 3 decimals).
Transcribed Image Text:X Open spreadsheet Complete the equation below for an estimated regression equation developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP) (to 3 decimals). R/IP = SO/IP + HR/IP a. Use the F test to determine the overall significance of the relationship. Compute F test statistic (to 2 decimals). The p-value is (to 3 decimals). What is your conclusion at the .05 level of significance? a significant overall relationship. b. Use the t test to determine the significance of each independent variable. Compute the t test statistic for the significance of SO/IP (to 2 decimals). There is + The p-value is (to 3 decimals). What is your conclusion at the .05 level of significance? significant. SO/IP is The p-value is î Compute the t test statistic for the significance of HR/IP (to 2 decimals). (to 3 decimals).
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