Question

A developmental psychologist is interested in whether there is a relationship between the grades of college students and the amount of time parents or other care givers spent reading to them when they were preschoolers. A random sample of 8 psychology majors is recruited for the study and the results are shown in the following table. Student Reading Time (hrs/wk) Grade Point Average (GPA) 1.6 2.0 3.9 (a) Assuming a linear relationship exists, derive the least squares regression line for predicting GPA from Reading Time. | X + (b) What GPA would you predict for a student with a reading time of 7 hrs/wk?

Answer 1

student	x	y	x2	y2	xy
1	0	1.6	0	2.56	0
2	4	2	16	4	8
3	3	2.3	9	5.29	6.9
4	0	2.8	0	7.84	0
5	5	3.3	25	10.89	16.5
6	10	3.5	100	12.25	35
7	8	3.8	64	14.44	30.4
8	9	3.9	81	15.21	35.1
Total=	39	23.2	295	72.48	131.9

X: Reading time Chrs/wk) 7. Grade point Averages (GPA) EX2 = 295, 542 = 72.48 {X=39 EXY = 131-9 { y = 23.2 n=8 X = {X = 39 = 4.875 nx2= 8 (4.875)2 = 9o.125 T = Ey - 23.2 = 2.9 Sx²= {X²-nx? - 295-190.125 = 104.875 Sru IXY - X Y = 131.9 -(4.875) (2.9) - 16.4875 - 14.1375 Sxy= 2.35)

sqe are regression line is The equation of least ŷ = bxta where b=slope a= intercept b= Sxy Sx² 0.16 = 3.35 14.98 b= a = Ý - by = 2.9 - (0.16) (4.875) = 2.9 - 0.76 la = 2.14 | for predicting GP A from The least square regression line reading time is ☺ - ax + b - y = /2.14 ) x +[0.16 / 6 is predicted GPA for a student with reading time of this I wk ie. x= 7 0.14 X +0.16 = 2.14(H) +0.16 ŷ = 14.95 + 0.16 19 = 15.11 The GPA for a student with reading time of 7 hrs/wk is 15.11