2.14 ( Sections 2.3.1, 2.4.1) Consider the data set of Exercise 1.11 on student

Question

2.14 ( Sections 2.3.1, 2.4.1) Consider the data set of Exercise 1.11 on student learning, with FGPA and SATuis scores of ten students. We investigate how far the FGPA scores of these students can be ex- plained in terms of their SATM scores. a. Regress the FGPA scores on a constant and PANI XR111STU SATM and compute a, b, and s2. b. Perform 5% significance tests on a and b. c. Construct 95% interval estimates for and . d. Make a point prediction of the FGPA score for a student with SATM score equal to 6.0. Construct also a 95% prediction interval. e. Discuss the conditions needed to be confident about these predictions.

Explanation / Answer

a)

FGPA^ = a + b * SATM

FGPA^ = -0.3287 + 0.5176 * SATM

s^2 = 0.289292

b)

p-value of both a and b > 0.05

we fail to reject the null hypothesis

c)

95% confidence interval

d)

FGPA^ = -0.3287 + 0.5176 * SATM

FGPA^ = -0.3287 + 0.5176 * 6

= 2.7769

SUMMARY OUTPUT Regression Statistics Multiple R 0.341562822 R Square 0.116665161 Adjusted R Square 0.006248307 Standard Error 0.537858825 Observations 10 ANOVA df SS MS F Significance F Regression 1 0.305662676 0.305662676 1.056588341 0.334067651 Residual 8 2.314336924 0.289292115 Total 9 2.6199996 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.328697634 2.940503962 -0.111782755 0.913749464 -7.109511931 6.452116663 SATM 0.517581069 0.503530146 1.027904831 0.334067651 -0.643561529 1.678723668

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