Question

In baseball a teams success is often thought to be a function of the team's hitting and pitching performance. One measure of hitting performance is the number of home runs that team hits, and one measure of pitching performance is the earned run average for the teams pitching staff. It is generally believed that teams that hit more home runs and have a lower earned run average will win a higher percentage of games played. The following data show the proportion of games won, the number of home runs (HR), and the earned run average (ERA) for the 16 teams in the National League for the 2003 Major League Baseball season.

	Team	Won	HR	ERA
	Arizona	0.519	152	3.857
	Atlanta	0.623	235	4.106
	Chicago	0.543	172	3.842
	Cincinnati	0.426	182	5.127
	Colorado	0.457	198	5.269
	Florida	0.562	157	4.059
	Houston	0.537	191	3.880
	Los Angeles	0.525	124	3.162
	Milwaukee	0.420	196	5.058
	Montreal	0.512	144	4.027
	New York	0.410	124	4.517
	Philadelphia	0.531	166	4.072
	Pittsburgh	0.463	163	4.664
	San Diego	0.395	128	4.904
	San Francisco	0.621	180	3.734
	St Louis	0.525	196	4.642
Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs.

1. Could someone please help me calculate the critical value of the model?

2. Also, I need to find the conclusion. I limited it down to these two. Could you please explain the reason for a or b?

a. Do not reject null hypothesis. there is not significant relationship between HR and wins

b. Do not reject null hypothesis. There is a significant relationship between ERA and wins

Thanks so much for your help. Will give you 5 stars

Answer 1

So, as we can see the mutliple regression equation is as followed:

y=0.71+0.0014x₁-0.103x₃+e

1. F_critical= 39.374

2. a) We do not reject the null hypothesis because according to the decision rule when p-value <0.05 the result is significant and we may not reject the null hypothesis. (0.00007< 0.05)

b) Similarly, here we do not reject the null hypothesis because according to the decision rule when p-value <0.05 the result is significant and we may not reject the null hypothesis. (0.0000021< 0.05)