With the data in the accompanying table, estimate GPA = beta_0 + beta_1 GRE + ep

Question

With the data in the accompanying table, estimate GPA = beta_0 + beta_1 GRE + epsilon, where GRE is a student's score on the math portion of the Graduate Record Examination score and GPA is the student's grade point average in graduate school. Use Table 2. a. Construct the 90% confidence interval for the expected GPA for an individual who scored 726 on the math portion of the GRE. b. Construct the 90% prediction interval for the GPA for an individual who scored 726 on the math portion of the GRE.

Explanation / Answer

Using technology, the regression equation is: GPA=-0.404+0.005424 GRE

a. For a 90% confidence interval, alpha=0.10. Because, n=8, df=n-2=6. The critical t value at 6 df and alpha/2=0.05 is 1.943.

For xp=726 (individual who scored 726 on the math portion of GRE), the point estimate for the mean score of all individuals with 726 on math portion of GRE is as follows:

yphat=-0.404+0.005424(726)=3.53

The end point sof the confidence interval is:

yphat+-talpha/2.se sqrt[1/n+(xp-xbar)^2/Sxx], where, Sxx=sigma xi^2-(sigmaxi)^2/n, se is stanadrd error of estimate, and the value is obtained from the technology output of regression analysis.

=3.53+-1.943.0.228730 sqrt[1/8+(726-719.8)^2/[4156766-(5758)^2/8]

=(3.37,3.69)

b. The 90% prediction interval is:yphat+-talpha/2. se sqrt[1+1/n+(xp-xbar)^2/Sxx]

=3.53+-1.943.0.228730 sqrt[1+1/8+(726-719.8)^2/[4156766-(5758)^2/8]

=(3.06,4.01)

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