Question

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

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.)

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