Question

The computer-science aptitude score, x, and the achievement score, y (measured by a comprehensive final), were measured for 20 students in a beginning computer-science course. The results were as follows.

x	5	15	19	12	23	20	14	21	18	15	17	16	9	5	6	19	19	10	20	13
y	19	19	24	36	27	26	25	28	17	27	21	24	18	18	14	28	21	22	20	21

(a) Find the equation of the line of best fit. (Round your slope to four decimal places and your y-intercept to three decimal places.)
= + x

(b) Find s_e². (Round your answer to two decimal places.)

Answer 1

(a)

To find the equation of the line of best fit,

	x	y	x2	y2	xy
	5	19	25	361	95
	15	19	225	361	285
	19	24	361	576	456
	12	36	144	1296	432
	23	27	529	729	621
	20	26	400	676	520
	14	25	196	625	350
	21	28	441	784	588
	18	17	324	289	306
	15	27	225	729	405
	17	21	289	441	357
	16	24	256	576	384
	9	18	81	324	162
	5	18	25	324	90
	6	14	36	196	84
	19	28	361	784	532
	19	21	361	441	399
	10	22	100	484	220
	20	20	400	400	400
	13	21	169	441	273
Σ	296	455	4948	10837	6959

(b)

Form the estimated linear equation find out estimated-y for all x i.e. put respective x in the regression equation.

	x	y
	5	19	18.8625	0.1375	0.018906
	15	19	22.8295	-3.8295	14.66507
	19	24	24.4163	-0.4163	0.173306
	12	36	21.6394	14.3606	206.2268
	23	27	26.0031	0.9969	0.99381
	20	26	24.813	1.187	1.408969
	14	25	22.4328	2.5672	6.590516
	21	28	25.2097	2.7903	7.785774
	18	17	24.0196	-7.0196	49.27478
	15	27	22.8295	4.1705	17.39307
	17	21	23.6229	-2.6229	6.879604
	16	24	23.2262	0.7738	0.598766
	9	18	20.4493	-2.4493	5.99907
	5	18	18.8625	-0.8625	0.743906
	6	14	19.2592	-5.2592	27.65918
	19	28	24.4163	3.5837	12.84291
	19	21	24.4163	-3.4163	11.67111
	10	22	20.846	1.154	1.331716
	20	20	24.813	-4.813	23.16497
	13	21	22.0361	-1.0361	1.073503
Σ					396.4958

The standard error is given by,