1. Entry Task What is the slope of the following lines? 1) 2y = 8x - 70
Answers 4 -4

2. OBJECTIVES 2-2 LINEAR REGRESSION
Banking
5/21/2018
2-2 LINEAR REGRESSION
OBJECTIVES
Be able to fit a regression line to a scatterplot.
Find and interpret correlation coefficients.
Make predictions based on lines of best fit.
Chapter 1

3. Key Terms line of best fit linear regression line least squares line
Banking
5/21/2018
Key Terms
line of best fit
linear regression line
least squares line
domain
range
interpolation
extrapolation
correlation coefficient
strong correlation
weak correlation
moderate correlation
Chapter 1

4. How can the past predict the future?
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5/21/2018
How can the past predict the future?
The trends shown by scatterplots can be used to predict the future. But making a prediction without a line of best fit to guide you would be arbitrary.
What can you tell about the sign of the correlation coefficient and the slope of the regression line?
Chapter 1

5. Banking
5/21/2018
Example 1
Find the equation of the linear regression line for Rachael’s scatterplot in Example 1 from Lesson Round the slope and y-intercept to the nearest hundredth. The points are given below.
(65, 102), (71, 133), (79, 144), (80, 161), (86, 191),
(86, 207), (91, 235), (95, 237), (100, 243)
Chapter 1

6. CHECK YOUR UNDERSTANDING
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5/21/2018
CHECK YOUR UNDERSTANDING
Find the equation of the linear regression line of the scatterplot defined by these points: (1, 56), (2, 45), (4, 20), (3, 30), and (5, 9). Round the slope and y-intercept to the nearest hundredth.
y = -11.9x
Chapter 1

7. Banking
5/21/2018
Example 2
Interpret the slope as a rate for Rachael’s linear regression line. Use the equation from Example 1.
The slope represents the bottles sold per degree. She can’t sell .44 bottles so she will sell approximately 4 bottles per degree.
Chapter 1

8. CHECK YOUR UNDERSTANDING
Banking
5/21/2018
CHECK YOUR UNDERSTANDING
Approximately how many more water bottles will Rachael sell if the temperature increases 2 degrees? 9
Chapter 1

9. Banking
5/21/2018
EXAMPLE 3
Rachael is stocking her concession stand for a day in which the temperature is expected to reach 106 degrees Fahrenheit. How many water bottles should she pack?
We will use y = 4.44x – to find the approximation.
y = 4.44 (106) – =
She should stock 283 bottles.
Chapter 1

10. Correlation Coefficient
The correlation coefficient, r , is a number between -1 and 1 and judges how closely the line fits the data. Negative numbers show negative correlations, and positive numbers show positive correlations. If the number is near 0, there is little or no correlation. If the number is above .75 there is strong correlation. Weak correlation occurs if the absolute value is between 0 and .3.

11. Turn on Correlation Coefficient
Then hit enter twice

12. Banking
5/21/2018
EXAMPLE 4
Find the correlation coefficient to the nearest hundredth for the linear regression for Rachael’s data. Interpret the correlation coefficient.
.97 – Rachael
.99 – other one
Chapter 1

13. Homework
P. 73 #2,3,4,6,7,8