Question

The following table contains the ACT scores and the GPA for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 2.& 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 a) Estimate the relationship between GPA and ACT using OLS: that is, obtain the intercept and slope estimates in the equation GPA-B0+ B1 ACT b) Comment on the interpretation and direction of the relationship. c) How much higher is the GPA predicted to be if the ACT score is increased by five points? d) How much of the variation in GPA for these eight students is explained by ACT?

Answer 1

U GAY ALT X. (xi - 5)/17 - 9) | (x-7)(4:4) | (x: - 2)² (Y;-92 28 Student Ly 21 -4.97 -0.41 20 -37 049 -0.35 24 3.0 24 0.13 0.03 021 3.5 0.33 1.13 27 0.29 3.6 29 1.22 3.0 | 25 2-7 -0-51 25 0.44 13.2 130 4.13 1o.ug 2-02 ES81 X= 25.87 - dns noro 23.72 3.50 0.02 1.23 9.80 0.76 0.76 17.- 6 0.17 0.04 0.04 0.8 0.15 0:04 0.26 0.24 0.39 -0.4 3.13 -0.97 -0.92 0.13 - 3.21 B = {(x; -%) (4:- Ý {(xi-X12. 13, 5.81 0.102. 56.9 Bo = 9 - BIX so = 3.21 - (0.102) (25-87) Bo= 0.571 GPA 0.57 + 0.102 ACT b) The & GPA and ACT are positively. related The wefficient of ACT implies that aone on an annage a unit increase in ALT will increase aPA by 0.102 unit. c) GPA will increas by 10.102. (s) = 0.51 d) R² [{(x,-814-93] {(x, y)² E1%-91² (56.9 (1.02) by =) R² = (5.812 0.58

2 nalne Using the con e2 of say that. GPA is explained in the variation 588) by ACT. of