Question: Assume that a sports writer wishes to set up a fairly simple ‘predictor' of success of the several softball teams in a league. He plans to use rated overall strength of team pitching' as \(X_{1}\) (1=very strong: 9= very weak) and rated 'overall strength of team hitting' as \(X_{2}\) (1= very strong, 9= very weak) as the two predictors of final standings \({{Y}_{\text{predicted }}}\) (1= best in the league; 8=bottom of league). With a little guidance from a statistician friend, he collects data from previous years, makes the necessary calculations and obtains the following key information to write his multiple regression equation:

Correlation between pitching strength and final standings: \(r_{X1/Y} = r_{p/f} =.68\), and, \(r^{2}=.46\)

Correlation between hitting strength and final standings: \({{r}_{X2/Y}}={{r}_{h/f}}=.59\), and, \({{r}^{2}}=.35\)

Correlation between pitching strength and hitting strength: \(r_{X 1/ X 2} = r_{p/h}=.38\), and, \(r^{2}=.14\)

\(b_{1}=\) Pitching \(=.61\)

\(b_{2}=\) Hitting \(=.47\)

\(a=-1.0\)

The needed regression equation is: \(\quad \mathrm{Y}_{\text {(predicicl) }}=b_{1} \mathrm{X}_{1}+b_{2} \mathrm{X}_{2}+a\)

Using the above information. what would be the predicted standing rounded that is the 'reverse’ of the team in Q51 and had a highly rated team pitching: score 1 and poorly rated team hitting score of 7?

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