Question

For the data set below,
(a) Determine the least-squares regression line.
(b) Compute the sum of the squared residuals for the least-squares regression line.

x 20 30 40 50 60
___________________
y 106 95 82 70 54

(a) Determine the least-squares regression line.

^
y =[]x +[] ( 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 = 133 - 1.29 x
Sample size: 5
R (correlation coefficient) = -0.99787352
R-sq = 0.99575156
Estimate of error standard deviation: 1.5383974

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	133	2.0639767	≠ 0	3	64.438711	<0.0001
Slope	-1.29	0.048648398	≠ 0	3	-26.516803	0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	1664.1	1664.1	703.14085	0.0001
Error	3	7.1	2.3666667
Total	4	1671.2

Hence,

a) Regression line equation:

= (-1.29) x + 133

b) Sum of Squared residuals = SSE = 7.1