1. Line of Best Fit 4-8 Warm Up Lesson Presentation Lesson Quiz
Holt Algebra 1
Holt McDougal Algebra 1

2. Warm Up Identify the slope and the y-intercept. 1. y = 2x + 1
m = 2, b = 1 3 2 m= 3 2
, b = -4
Identify the correlation (positive, negative, or none) that you would expect to see between each pair of data sets.
3. a person’s height and shoe size
pos
4. the age of a car and its value
neg

3. Objectives Determine a line of best fit for a set of linear
data. Determine and interpret the correlation
coefficient.

4. Vocabulary residual least-squares line line of best fit
linear regression
correlation coefficient

5. A residual is the signed vertical distance between a data point and a line of fit.
The least-squares line for a data set is the line of fit for which the sum of the squares of the residuals is as small as possible.
A line of best fit is the line that comes closest to all of the points in the data set, using a given process.
Linear regression is a process of finding the least-squares line.

6. The correlation coefficient is a number r, where -1 ≤ r ≤ 1, that describes how closely the points in a scatter plot cluster around a line of best fit.

7. In By using squares of residuals, positive and negative residuals do not “cancel out” and residuals with squares greater than 1 have a magnified effect on the sum.
Helpful Hint

8. Example1: Calculating Residuals
Two lines of fit for this data are y = 2x + 2 and y = x + 4. For each line, find the sum of the squares of the residuals. Which line is a better fit? X 1 2 3 4 Y 7 5 6 9

9. Example1: Continued
Find the residuals
y = x + 4:
Sum of squared residuals:
(2)2 + (–1)2 + (–1)2 + (1)2
= 7

10. Example1: Continued
Find the residuals
y = 2x + 2:
Sum of squared residuals:
(3)2 + (–1)2 + (–2)2 + (-1)2
= 15
The line y = x + 4 is a better fit.

11. Check It Out! Example 1
Two lines of fit for this data are
For each line, find the sum of the squares of the residuals. Which line is a better fit?
Y = - 2 1
x + 6 and y = -x + 8

12. Check It Out! Example 1 Continued
Find the residuals. 2 1
y = –
x + 6 :
Sum of squared residuals:
(–2)2 + (2)2 + (–2)2 + (2)2
= 16

13. Check It Out! Example 1 Continued
Find the residuals.
y = –x + 8:
Sum of squared residuals:
(–3)2 + (2)2 + (–1)2 + (4)2
= 30
y = - 2 1
The line
x + 6
is a better fit

14. Lesson Quiz :
The table shows time spent on homework and number of incorrect quiz answers for several students.
Two lines of fit are y = -x + 11 and y = -0.5x + 8. Find the sum of the squares of the residuals for each line. Which line is a better fit?
18; 20; y = -x + 11