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 Bat

x2 = Doubles/Times at Bat

x3 = Triples/Times at Bat

x4 = Home Runs/Times at Bat

x5= Strike Outs/Times at Bat

Estimate the Batting Average when Run Score = 0.123, Doubles = 0.040, Triples = 0.0045 ,  Home Runs = 0.009 and Strike Outs = 0.189

DATA:

Batting Average	RS/Times at Bat	Doubles/Times at Bat	Triples/times at bat	HR/Times at Bat	SO/Times at Bat
0.283	0.144	0.049	0.012	0.013	0.086
0.276	0.125	0.039	0.013	0.002	0.062
0.281	0.141	0.045	0.021	0.013	0.074
0.328	0.189	0.043	0.001	0.03	0.032
0.29	0.161	0.044	0.011	0.07	0.076
0.296	0.186	0.047	0.018	0.05	0.007
0.248	0.106	0.036	0.008	0.012	0.095
0.228	0.117	0.03	0.006	0.003	0.145
0.305	0.174	0.05	0.008	0.061	0.112
0.254	0.094	0.041	0.005	0.014	0.124
0.269	0.147	0.047	0.012	0.009	0.111
0.3	0.141	0.058	0.01	0.011	0.07
0.307	0.135	0.041	0.009	0.005	0.065
0.214	0.1	0.037	0.003	0.004	0.138
0.329	0.189	0.058	0.014	0.011	0.032
0.31	0.149	0.05	0.012	0.05	0.06
0.252	0.119	0.04	0.008	0.049	0.233
0.308	0.158	0.038	0.013	0.003	0.068
0.342	0.259	0.06	0.016	0.085	0.158
0.358	0.193	0.066	0.021	0.037	0.083
0.34	0.155	0.051	0.02	0.012	0.04
0.304	0.197	0.052	0.008	0.054	0.095
0.248	0.133	0.037	0.003	0.043	0.135
0.367	0.196	0.063	0.026	0.01	0.031
0.325	0.206	0.054	0.027	0.01	0.048
0.244	0.11	0.025	0.006	0	0.061
0.245	0.096	0.044	0.003	0.022	0.151
0.318	0.193	0.063	0.02	0.037	0.081
0.207	0.154	0.045	0.008	0	0.252
0.32	0.204	0.053	0.017	0.013	0.07
0.243	0.141	0.041	0.007	0.051	0.264
0.317	0.209	0.057	0.03	0.017	0.058
0.199	0.1	0.029	0.007	0.011	0.188
0.294	0.158	0.034	0.019	0.005	0.014
0.221	0.087	0.038	0.006	0.015	0.142
0.301	0.163	0.068	0.016	0.022	0.092
0.298	0.207	0.042	0.009	0.066	0.211
0.304	0.197	0.052	0.008	0.054	0.095
0.297	0.16	0.049	0.007	0.038	0.101
0.188	0.064	0.044	0.007	0.002	0.205
0.214	0.1	0.037	0.003	0.004	0.138
0.218	0.082	0.061	0.002	0.012	0.147
0.284	0.131	0.049	0.012	0.021	0.13
0.27	0.17	0.026	0.011	0.002	0
0.277	0.15	0.053	0.005	0.039	0.115

Possible Answers:

• A.

  0.223

• B.

  0.057

• C.

  0.043

• D.

  0.229

Answer 1

from excel:data-data analysis: regression:

batting average =0.1832+0.4467*Run Score+0.9909*Doubles+0.6216*Triples+0.2737*HR-0.2846*SO

therefore predicted

batting average =0.1832+0.4467*0.123+0.9909*0.04+0.6216*0.0045+0.2737*0.0099-0.2846*0.189

=0.229