Question

For the data set shown​ below, complete parts​ (a) below. x 3 4 5 7 8 y 5 6 7 11 14 ​  Find the estimates of beta 0 and beta 1. beta = -1.070 ​beta 1=1.791 Compute the standard​ error, the point estimate for sigma. s Subscript = ​(Round to four decimal places as​ needed.)

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -1.0697674 + 1.7906977 x
Sample size: 5
R (correlation coefficient) = 0.98194797
R-sq = 0.96422182
Estimate of error standard deviation: 0.82593616

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-1.0697674	1.1370801	≠ 0	3	-0.94080219	0.4162
Slope	1.7906977	0.19915089	≠ 0	3	8.9916628	0.0029

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	55.153488	55.153488	80.85	0.0029
Error	3	2.0465116	0.68217054
Total	4	57.2

Hence,

b) Standard error = 0.8259