Question

x: 1.5, 1, .25, .5

y: 3.75, 2, 1, 1.75

1) what is the % variation in y explained by the regression

2) test the null hypothesis that the slope =0 with the alternative that slope is not =0 and using alpha =.01. write down the test p value and state your conclusion about the hypothesis.

Answer 1

necessary calculation for finding regression equation:-

x	y	x^2	y^2	xy
1.5	3.75	2.25	14.0625	5.625
1	2	1	4	2
0.25	1	0.0625	1	0.25
0.5	1.75	0.25	3.0625	0.875
sum=3.250	sum=8.500	sum=3.563	sum=22.13	sum=8.75

  

the regression equation be:-

y= 0.5009 + 1.9989 slope

necessary calculation table for calculating variation in y:-

y	FITS()	(y hat- y bar)^2	(y-y bar)^2
3.75	3.5	1.890625	2.640625
2	2.5	0.140625	0.015625
1	1	1.265625	1.265625
1.75	1.5	0.390625	0.140625
		sum=3.687	sum=4.063

so, the % variation in y explained by the regression:-

percent

b).hypothesis:-

calculation of test statistic:-

necessary calculation:-

x	y	FITS()	(y- y hat)^2	(x- x bar)^2
1.5	3.75	3.5	0.0625	0.472656
1	2	2.5	0.25	0.035156
0.25	1	1	4.44E-31	0.316406
0.5	1.75	1.5	0.0625	0.097656
sum=3.250			sum=0.375	sum=0.921875

test statistic:-

df= (n-2) = (4-2) = 2

p value = 0.0473 ( using p value calculator for df= 2 , t score= 4.4321,alpha = 0.01)

decision:-

p value = 0.0473 >0.01, so we fail to reject our null hypothesis.so, at 0.01 LOS there is not sufficient evidence to say that the slope is different from 0.

***if you have any doubt regarding the problem please write it in the comment section.if you are satisfied please give me a LIKE vote if possible...