Problem 34 BB
LeastSquares Property According to the leastsquares property, the regression line minimizes the sum of the squares of the residuals. Refer to the data in Table.
a. Find the sum of squares of the residuals.
b. Show that the regression equation results in a larger sum of squares of residuals.
Table Shoe Print Lengths and Heights of Males
Answer:
Step 1 of 1</p>
According to the leastsquares property, the regression line minimizes the sum of the squares of the residuals. Refer to the data in Table.
a. The sum of squares of the residuals.
Shoe print(x) 
Height(y) 
xy 
x2 

29.7 
175.3 
5206.41 
882.09 

29.7 
177.8 
5280.66 
882.09 

31.4 
185.4 
5821.56 
985.96 

31.8 
175.3 
5574.54 
1011.24 

27.6 
172.7 
4766.52 
761.76 

SUM 
150.2 
886.5 
26649.69 
4523.14 
AVERAGE 
30.04 
177.3 
,
n = 5 , , ,
= = 1.7274
= 125.4089
Therefore,
Shoe print(x) 
Height(y) 
Predicted Y

(y 
29.7 
175.3 
176.7126662 
1.995626 
29.7 
177.8 
176.7126662 
1.182295 
31.4 
185.4 
179.6493352 
33.07015 
31.8 
175.3 
180.3403162 
25.40479 
27.6 
172.7 
173.0850162 
0.148237 
SUM 
886.5 
61.80109 