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Least-Squares Property According to the least-squares
Chapter 10, Problem 34BB(choose chapter or problem)
Least-Squares Property According to the least-squares 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 \(y^{\wedge}=120+2.00 x) results in a larger sum of squares of residuals.
Equation Transcription:
Text Transcription:
y^{\wedge}=120+2.00 x
Questions & Answers
QUESTION:
Least-Squares Property According to the least-squares 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 \(y^{\wedge}=120+2.00 x) results in a larger sum of squares of residuals.
Equation Transcription:
Text Transcription:
y^{\wedge}=120+2.00 x
ANSWER:Answer:
Step 1 of 1
According to the least-squares 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 |