Question

1. In baseball, is there a linear correlation between batting average and home run percentage? A random sample of 7 professional baseball players gave the following information: Batting average: Home run percentage: 1.4 3.6 5.5 3.8 3.5 7.3 5.0 Use a 0.05 significance level to determine if there is a linear correlation between batting average and home run percentage. What is the best estimate for the home run percentage of a player who has a batting average of 0.300 0.243 0.259 0.286 0.263 0.268 0.339 0.299 The Fish and Game Department stocked Lake Lulu with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows: Catfish 2. Bass USS 85 Pike 75 12 Use a 0.01 significance level to test the claim that the distribution of fish changed over the five years.

Answer 1

Solution-

1. After running regression analysis in the excel, regression output is-

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.94807346 0.898843285 0.878611942 0.647451486 7 ANOVA df MS F Significance F Regression Ricdual Total 18.62403287 18.62403 44.42826 0.001147461 2.095967132 0.419193 20.72 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept X Variable 1 11.1228302 2.326750508 4.78041 0.004969 -17.10393279 -5.141727606 55.16597414 8.276403555 6.665452 0.001147 33.89080149 76.44114678

Regression equation is-

Y = -11.1228 + 55.16597 * X

When X = 0.3, then Y = -11.1228 + 55.16597 * 0.3

= 5.427

To test whether linear relationship exists, we have hypotheses as-

H0 - There is no linear relationship

Ha - There is a linear relationship

P-value from the anova table above = 0.001147

As this is less than 0.05, hence we reject the null hypothesis at 5% level of significance. Thus there exists linear relationship.

Answer

thanks!