Question

For the data set shown​ below

x   y
20   98
30   95
40   91
50   83
60   70

​(a) Use technology to find the estimates of β0 and β1.

β0≈b0equals=114.60

​(Round to two decimal places as​ needed.)

β1≈b1=−0.68

​(Round to two decimal places as​ needed.)

​(b) Use technology to compute the standard​ error, the point estimate for σ.

Se=__?__

​(Round to four decimal places as​ needed.)

Answer 1

X	Y	XY	X²	Y²
20	98	1960	400	9604
30	95	2850	900	9025
40	91	3640	1600	8281
50	83	4150	2500	6889
60	70	4200	3600	4900
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
200	437	16800	9000	38699

Sample size, n =	5
SSxx = Ʃx² - (Ʃx)²/n =	1000
SSyy = Ʃy² - (Ʃy)²/n =	505.2
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	-680

a) Slope, b1 = SSxy/SSxx = -0.68

y-intercept, b0 = y̅ -b1* x̅ = 114.6

b) Sum of Square error, SSE = SSyy -SSxy²/SSxx = 42.8

Standard error, se = √(SSE/(n-2)) = 3.7771

Using Excel output is:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.956703
R Square	0.915281
Adjusted R Square	0.887041
Standard Error	3.777124
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	462.4	462.4	32.41121	0.010744
Residual	3	42.8	14.26667
Total	4	505.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	114.6	5.067544	22.61451	0.000189	98.47281	130.7272
X	-0.68	0.119443	-5.69308	0.010744	-1.06012	-0.29988