Question

A baseball analyst is trying to predict the number of wins of a baseball team by using the team’s earned run average (ERA). He used data from 12 major league baseball teams and developed the following regression model and ANOVA table. Use Alpha = 0.05Perform a t-test to determine if there is a linear relationship between the number of wins and ERA. The regression equation is y=3+1.5x. and Sb₁ = .22

Source                      df                            SS                     MS                 F

Regression                1                              1346                1346              31.01

Error                        10                               434                   43.4              

Total                         11                             1780      

Answer 1

Let the regression model that is being estimated be

where y= the number of wins of a baseball team

x= the team’s earned run average (ERA)

to determine if there is a linear relationship between the number of wins and ERA using the t test, we want to tets the following hypotheses

The significance level to perform this test is

The estimated regression equation is

The estimated value of the slope coefficient is

the estimated standard error of slope is

The hypothesized value of the slope is

The test statistic is

This is a 2 tailed test (The alternative hypothesis has "not equal to")

The right tail critical value for is

The sample size is n=12. The degrees of freedom are n-2=12-2=10.

Using the t tables for df=10 and the area under the right tail=0.025, we get

The critical values are -2.228 and +2.228

We will reject null hypothesis if the test statistic lies outside the interval (-2.228 and +2.228).

Here, the test statistic is 6.818 and it lies outside the interval (-2.228 and +2.228). Hence we reject the null hypothesis.

ans: Reject the H₀. There is a significant  linear relationship between the number of wins and ERA.