1. 7.1 Draw Scatter Plots and Best Fitting Lines
Pg. 255
Notetaking Guide

2. Vocabulary Scatter Plot Positive Correlation Negative Correlation
A graph of a set of data pairs (x, y)
Positive Correlation
The relationship between paired data when “y” tends to increase as “x” increases
Negative Correlation
The relationship between paired data when “y” tends to decrease as “x” increases

3. Vocabulary (cont.) Correlation Coefficient Best Fitting Line
A number, denoted by “r”, from - 1 to 1 that measures how well a line fits a set of data pairs (x, y)
Best Fitting Line
The line that lies as close as possible to all the date points
Linear Regression
A method for finding the equation of the best fitting line, or regression line, which expresses the linear relationship between the independent variable “x” and the dependent variable “y”

4. Vocabulary (cont.) Median-Median Line Algebraic Model Inference
A median-median line is a linear model used to fit a line to a data set. The line is fit only to summary points, “key” points calculated using medians.
Algebraic Model
An expression, equation, or function that represents data or a real-world situation
Inference
A logical conclusion that is derived from know data

5. Example #1 (Correlation Coefficients)
Describe the data as having a positive correlation, a negative correlation, or approximately no correlation. Tell whether the correlation coefficient for the data is closest to – 1, , - 0.5, 0, 0.5, 0.75, or 1.
a. b.
Strong Negative Correlation
r =
Weak Positive Correlation
r = 0.5

6. Checkpoint You complete 1 & 2 Use the following scale for “r”
- 1, , - 0.5, 1, 0.5, 0.75, 1

7. Example #2 (Best-Fitting Line)
Approximate the best fitting line
Draw a _____________
Sketch the best fitting line
Choose two points on the scatter plot. {(1, 722), and (2, 750)}
Write an equation of the line. We need the slope and y-intercept x 1 2 3 4 5 6 7 y
722
763
772
826
815
857
897

8. Example #2 (cont.)
Slope
Now use the point-slope formula with one of your points
(Only use one of your points (1, 722), & m = 28)

9. Checkpoint
Use the table to answer the questions

10. Example #3 (Median-Median Line)
Find the equation for the median-median line
** Make sure your data is in order from least to greatest values “by the x values”
Divide data into 3 equal size groups (if not possible make the first and last groups equal size and the center group smaller)

11. Example #3 (cont.) Create a table of your values
Create a summary point for each group (these are your x and y medians)
Group
x’s
y’s
Median 1
1, __, 3
__, 34, 40 __ 2
5, 6, __
35, 60, __ 3
__, 10, 11
45, __, 60
Group 1:
(__, __)
Group 2:
Group 3:

12. Group 1:
(2, 34)
Group 2:
(6, 60)
Group 3:
(10, 50)
Example #3 (cont.)
Determine the equation of the line between the two outer (group 1 and group 3) summary points by finding the slope between the two points and then using the slope and one point in the point slope formula

13. Example #3 (cont.) Final Step Middle summary point (6, 60)
Move the equation from group 1 and group 3 one-third of the way to the middle summary point
Middle summary point (6, 60)
Use equation from group 1 and group 3 to find the predicted value for x = 6
One third of the difference between y = 60 and y = 42
Add the difference to the equation
Group 1:
(2, 34)
Group 2:
(6, 60)
Group 3:
(10, 50)

14. Checkpoint
Find the equation of the median-median line

15. Practice (median-median)
(1, 22), (2, 27), (2, 20), (3, 15), (4, 19), (5, 10), (5, 14), (6, 9), (8, 7), (8, 11), (8, 13), (9, 5)

16. Practice (median-median)
(12, 42), (15, 72), (17, 81), (11, 95), (8, 98), (14, 78), (9, 83), (13, 87), (13, 92)

17. Homework NTG pg. 260, 1 – 13 all