Concept explainers
To find: The least squares regression line for the given data and the sum of the squared differences.
Answer to Problem 22E
The equation is
Explanation of Solution
Given:
The data points are
Calculation:
Let the general equation of the least squares regression line be
In order to determine value of the coefficients of a and b in the set of equations (1), construct a table as shown below:
x | y | ||
17 | 6.137 | 104.329 | 289 |
18 | 6.217 | 111.906 | 324 |
19 | 6.290 | 119.510 | 361 |
20 | 6.340 | 126.800 | 400 |
Table 1
Substitute the values from the above table into the set of equations (1).
Simplify the set of equations to determine the values of a and b.
So, the equation of the least squares regression line becomes,
In order to calculate the sum of the differences, determine the value of
x | y | |||
17 | 6.137 | 6.1437 | -0.0067 | 0.00004489 |
18 | 6.217 | 6.2119 | 0.0051 | 0.00002601 |
19 | 6.290 | 6.2801 | 0.0099 | 0.00009801 |
20 | 6.340 | 6.3483 | -0.0083 | 0.00006889 |
Table 2
From table 2, the sum of the differences is 0.0002378.
Chapter 13 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning