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≈b0=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=3.7771

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

​(c) Assuming the residuals are normally​ distributed, use technology to determine sb1.

sb1=__?__

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

Answer 1

Following is the output of regression line generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.956703233
R Square	0.915281077
Adjusted R Square	0.887041436
Standard Error	3.777124126
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	462.4	462.4	32.41121495	0.010744254
Residual	3	42.8	14.26666667
Total	4	505.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	114.6	5.067543784	22.61450614	0.000189348	98.47281401	130.727186
X	-0.68	0.119443152	-5.693084836	0.010744254	-1.06012142	-0.299878581

-------------------------

​(a)

β0≈b0=114.60

β1≈b1=−0.68

​ (b)

Se=3.7771

​(c)

sb1=0.1194