Question

You decided to join a fantasy Baseball league and you think the best way to pick your players is to look at their Batting Averages. You want to use data from the previous season to help predict Batting Averages to know which players to pick for the upcoming season. You want to use Runs Score, Doubles, Triples, Home Runs and Strike Outs to determine if there is a significant linear relationship for Batting Averages.You collect data to, to help estimate Batting Average, to see which players you should choose. You collect data on 45 players to help make your decision.x1 = Runs Score/Times at Batx2 = Doubles/Times at Batx3 = Triples/Times at Batx4 = Home Runs/Times at Batx5= Strike Outs/Times at BatEstimate the Batting Average when Run Score = 0.123, Doubles = 0.040, Triples = 0.0045 , Home Runs = 0.009 and Strike Outs = 0.189DATA:Batting Average RS/Times at Bat Doubles/Times at Bat Triples/times at bat HR/Times at Bat SO/Times at Bat0.283 0.144 0.049 0.012 0.013 0.0860.276 0.125 0.039 0.013 0.002 0.0620.281 0.141 0.045 0.021 0.013 0.0740.328 0.189 0.043 0.001 0.03 0.0320.29 0.161 0.044 0.011 0.07 0.0760.296 0.186 0.047 0.018 0.05 0.0070.248 0.106 0.036 0.008 0.012 0.0950.228 0.117 0.03 0.006 0.003 0.1450.305 0.174 0.05 0.008 0.061 0.1120.254 0.094 0.041 0.005 0.014 0.1240.269 0.147 0.047 0.012 0.009 0.1110.3 0.141 0.058 0.01 0.011 0.070.307 0.135 0.041 0.009 0.005 0.0650.214 0.1 0.037 0.003 0.004 0.1380.329 0.189 0.058 0.014 0.011 0.0320.31 0.149 0.05 0.012 0.05 0.060.252 0.119 0.04 0.008 0.049 0.2330.308 0.158 0.038 0.013 0.003 0.0680.342 0.259 0.06 0.016 0.085 0.1580.358 0.193 0.066 0.021 0.037 0.0830.34 0.155 0.051 0.02 0.012 0.040.304 0.197 0.052 0.008 0.054 0.0950.248 0.133 0.037 0.003 0.043 0.1350.367 0.196 0.063 0.026 0.01 0.0310.325 0.206 0.054 0.027 0.01 0.0480.244 0.11 0.025 0.006 0 0.0610.245 0.096 0.044 0.003 0.022 0.1510.318 0.193 0.063 0.02 0.037 0.0810.207 0.154 0.045 0.008 0 0.2520.32 0.204 0.053 0.017 0.013 0.070.243 0.141 0.041 0.007 0.051 0.2640.317 0.209 0.057 0.03 0.017 0.0580.199 0.1 0.029 0.007 0.011 0.1880.294 0.158 0.034 0.019 0.005 0.0140.221 0.087 0.038 0.006 0.015 0.1420.301 0.163 0.068 0.016 0.022 0.0920.298 0.207 0.042 0.009 0.066 0.2110.304 0.197 0.052 0.008 0.054 0.0950.297 0.16 0.049 0.007 0.038 0.1010.188 0.064 0.044 0.007 0.002 0.2050.214 0.1 0.037 0.003 0.004 0.1380.218 0.082 0.061 0.002 0.012 0.1470.284 0.131 0.049 0.012 0.021 0.130.27 0.17 0.026 0.011 0.002 00.277 0.15 0.053 0.005 0.039 0.115Possible Answers:A. 0.223B. 0.057C. 0.043D. 0.229

Answer 1

The estimated value of the Batting Average is 0.229.

Explanation:

In this case regression analysis is to performed to determine if there is a significant linear relationship for Batting Averages with Runs Score, Doubles, Triples, Home Runs and Strike Outs.

The independent and dependent variables are as follows:

y = Batting Averages

x₁ = Runs Score/Times at Bat

x₂ = Doubles/Times at Bat

x₃ = Triples/Times at Bat

x₄ = Home Runs/Times at Bat

x₅= Strike Outs/Times at Bat

The regression analysis can be performed in Excel.

Consider the regression output attached.

The regression equation is as follows:

`y=0.183+0.447x_(1)+0.991x_(2)+0.622x_(3)+0.274x_(4)-0.285x_(5)`

Now estimate the Batting Average when Run Score (x₁) = 0.123, Doubles ( x₂) = 0.040, Triples (x₃) = 0.0045 , Home Runs ( x₄) = 0.009 and Strike Outs (x₅) = 0.189 as follows:

`y=0.183+0.447x_(1)+0.991x_(2)+0.622x_(3)+0.274x_(4)-0.285x_(5)`

`=0.183+(0.447\cdot 0.123)+(0.991\cdot 0.040)+(0.622\cdot 0.0045)\\+(0.274\cdot 0.009)-(0.285\cdot 0.189)\\\\=0.229021\\\\\approx 0.229`

Thus, the estimated value of the Batting Average is 0.229.