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	3	15	19	14	21	22	14	21	20	15	17	18	7	5	4	19	17	12	18	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.)

The computer-science aptitude score, x, and the achievement score, y (measured by a comprehensive final), were measured for 10 students in a beginning computer-science course. The results were as follows. Calculate the estimated standard error of regression, s_b1. (Give your answer correct to two decimal places.)

x	4	16	20	13	22	21	15	20	19	16
y	18	18	23	35	28	27	26	29	16	26

_______________

Answer 1

	x	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)
	3	19	136.89	14.0625	43.875
	15	19	0.09	14.0625	-1.125
	19	24	18.49	1.5625	5.375
	14	36	0.49	175.5625	-9.275
	21	27	39.69	18.0625	26.775
	22	26	53.29	10.5625	23.725
	14	25	0.49	5.0625	-1.575
	21	28	39.69	27.5625	33.075
	20	17	28.09	33.0625	-30.475
	15	27	0.09	18.0625	1.275
	17	21	5.29	3.0625	-4.025
	18	24	10.89	1.5625	4.125
	7	18	59.29	22.5625	36.575
	5	18	94.09	22.5625	46.075
	4	14	114.49	76.5625	93.625
	19	28	18.49	27.5625	22.575
	17	21	5.29	3.0625	-4.025
	12	22	7.29	0.5625	2.025
	18	20	10.89	7.5625	-9.075
	13	21	2.89	3.0625	2.975
sum	294	455	646.2	485.75	282.5
mean	14.7	22.75	sxx	syy	sxy
	slope=b1=sxy/sxx	0.437171154
	intercept=b0=ybar-(slope*xbar)	16.32358403

# Regression equation is

y^=bo+b1*x

y^=16.324+0.437*x

Ansb:

	x	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)
	4	18	158.76	43.56	83.16
	16	18	0.36	43.56	3.96
	20	23	11.56	2.56	-5.44
	13	35	12.96	108.16	-37.44
	22	28	29.16	11.56	18.36
	21	27	19.36	5.76	10.56
	15	26	2.56	1.96	-2.24
	20	29	11.56	19.36	14.96
	19	16	5.76	73.96	-20.64
	16	26	0.36	1.96	-0.84
sum	166	246	252.4	312.4	64.4
mean	16.6	24.6	sxx	syy	sxy
	slope=b1=sxy/sxx	0.255150555
	intercept=b0=ybar-(slope*xbar)	20.36450079
	SST	SYY	312.4
	SSR	sxy^2/sxx	16.431696
	SSE	syy-sxy^2/sxx	295.9683
	r^2	SSR/SST	0.0525983
	error variance s^2	SSE/(n-2)	98.656101
	S^2b1	s^2/sxx	0.390872
	standard error b1=se(b1)	sqrt(s^2b1)	0.6251976

#the estimated standard error of regression, sb1=0.63