1. Warm-Up
Write the equation of each line. A B
(1,2) and (-3, 7)

2. Correlation and Lines of Best Fit
Unit 8 - Statistics

3. Correlation
Correlation tells us about the LINEARITY of two quantitative variables
It is a number, “r”, that can be calculated and is always −1≤𝑟≤1.
The closer to 1 or -1 r is, the more linear the scatterplot of the two variables.

4. Values of “r”
Values close to +1 indicate a positive, linear correlation
Values close to 0 indicate no correlation or a non-linear pattern
Values close to -1 indicate a negative, linear correlation
r ≈ 0 (no linear correlation)
r = 1 (positive perfect)
r = -1 (negative perfect)

5. Match the r-value to it’s graph
𝑟=0.8 𝑟=−0.05 𝑟=−0.91 𝑟=0.57
Negative very weak
Positive strong
Positive weak
Negative stong
Remember, a low r-value doesn’t mean the variables are not related. It only tells us they are not LINEARLY related!

6. Lines of Best Fit
Most scatterplot are not perfectly linear, but are close enough for us to model with a line.
What is a line of Best Fit?
Line that approximates the data
Where is it on a scatterplot?
Through the “center” of the points
Why do we need one?
Predict outcomes that are not found in the data

7. Finding the Line of Best Fit
Plot the points.
Pick two “center” points and connect them with a line.
There should be about the same number of data points above and below the line you draw.
Use the two points to calculate a slope.
Calculate the y-intercept.
Use point-slope formula and convert to slope-intercept form.

8. Example #1
Approximate a line of best fit for the data. Predict what y would be in x is 20.
𝑚= 11−2 13−5 = 9 8 =1.125
𝑦−2=1.125 𝑥−5
𝑦 =1.125𝑥−3.625

9. Practice Modeling
y = 2.04x-2.36

10. Other models Match each graph with it’s line of best fit
𝑦= 𝑥 3 −2 𝑥 2 +3
𝑦= 2 𝑥
𝑦=− 𝑥−
𝑦=−2𝑥+3 A B C D