Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team andplayer 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 aparticular 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 following data show values for these statistics for a random sample of 20 pitchers from the American League for one full season.PlayerТeamWERASO/IPHR/IPR/IPVerlander, JDET242.401.000.090.29Beckett, JBOS1372.880.920.120.35Wilson, CTEX1672.930.930.080.40Sabathia, CΝY198.3.010.970.060.36Haren, DLAA16103.160.800.080.37McCarthy, BOAK3.330.720.070.42Santana, ELAA11123.390.770.100.42Lester, JBOS153.470.940.110.39Hernandez, FSEA14143.480.960.080.43Buehrle, MCWS133.600.540.090.46Pineda, MSEA103.731.000.120.43Colon, BNYY8104.000.830.140.53Tomlin, JCLE1274.260.530.140.47Pavano, CMIN134.300.450.090.54Danks, JCws8.124.320.790.110.53Guthrie, JBAL174.320.620.140.54Lewis, CTEX14104.410.830.170.51Scherzer, MDET154.420.880.140.51Davis, WTB11104.460.570.140.53Porcello, RDET144.750.570.100.56 a. What are the values of R? and R (to 3 decimals), if the average number of runs is the dependent variable and the average number of strikeoutsper inning pitched and the average number of home runs per inning pitched are the independent variables. Enter negative value as negativenumber.R/IP =SO/IP +HR/IPR?b. Does the estimated regression equation provide a good fit to the data? Explain. (to 1 decimal)The fit is - Select your answer - †because the nature of the data is able to explain% of the variability in the number of runs given upper inning pitched.c. Suppose the earned run average (ERA) is used as the dependent variable in part (a) instead of the average number of runs given up per inningpitched. What are the values of R? and R? (to 3 decimals). Enter negative value as negative number.ERA+SO/IP +HR/IPR =Does the estimated regression equation provide a good fit to the data? Explain. (to 1 decimal)The fit is- select your answer -ecause the nature of the data isto explainthe variability in+

The independent variables are SO/IP and HR/IP. The dependent variables are R/IP and ERA. We have to find the regression equation, R^2, adjusted R^2 and interpretation of R^2 for 2 different dependent variables. This is multiple regression model.EXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter SO/IP in one column, enter HR/IP in one column and enter R/IP in one column. Step 2: In Data, select Data Analysis and choose Regression. Step 3: In Input Variable Y Range: select R/IP. Step 4: In Input Variable X Range: select SO/IP and HR/IP. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) output: R/IP = 0.524 + (-0.253) SO/IP + 1.152 HR/IP. R2 = 0.606 Radj2= 0.559.The fit is good, because the nature of the data is able to explain 60.6% of the variability in the number of runs given up per inning pitched.EXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter SO/IP in one column, enter HR/IP in one column and enter ERA in one column. Step 2: In Data, select Data Analysis and choose Regression. Step 3: In Input Variable Y Range: select ERA. Step 4: In Input Variable X Range: select SO/IP and HR/IP. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) output: ERA = 3.980 + (-1.980) SO/IP + 11.960 HR/IP. R2= 0.656 Radj2= 0.616. The fit is good, because the nature of the data is able to explain 65.6% of the variability in the number of runs given up per inning pitched.