Question

A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on this test and performance in college. We have chosen a random sample of fifteen students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 1600 ) and her grade point average (from 0 to 4 ) for her first year in college. The data are shown below, with x denoting the score on the standardized test and y denoting the first-year college grade point average. A scatter plot of the data is shown in Figure 1. Standardized test score, x Grade point average, y 1020 3.03 910 2.67 1350 3.71 1250 3.38 1090 2.07 1290 2.84 940 2.40 870 2.26 1040 2.79 1210 2.77 1500 3.27 800 2.31 1410 3.05 1000 2.21 1500 3.07 Send data to Excel x 800 900 1000 1100 1200 1300 1400 1500 y 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 0 Figure 1 The value of the sample correlation coefficient r for these data is approximately 0.723 . Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult alist of formulas.) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least four decimal places. What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least four decimal places.

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	1020	3.03	1040400	9.1809	3090.6
	910	2.67	828100	7.1289	2429.7
	1350	3.71	1822500	13.7641	5008.5
	1250	3.38	1562500	11.4244	4225
	1090	2.07	1188100	4.2849	2256.3
	1290	2.84	1664100	8.0656	3663.6
	940	2.4	883600	5.76	2256
	870	2.26	756900	5.1076	1966.2
	1040	2.79	1081600	7.7841	2901.6
	1210	2.77	1464100	7.6729	3351.7
	1500	3.27	2250000	10.6929	4905
	800	2.31	640000	5.3361	1848
	1410	3.05	1988100	9.3025	4300.5
	1000	2.21	1000000	4.8841	2210
	1500	3.07	2250000	9.4249	4605
Total	17180	41.83	20420000	119.8139	49017.7

Sample size: n=15

Now,

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'=1.080975+0.001491*x