1. 4.5 Analyzing Lines of Fit

2. What We Will Learn Use technology to find lines of best fit
Distinguish between correlation and causation

3. Needed Vocab Linear regression: method used to find line of best fit
Line of best fit: line that best models a set of data
Correlation coefficient: value that tells how positive or negative the correlation is
Interpolation: using a graph to approximate a value between two known values
Extrapolation: using a graph to predict a value outside the range of known values
Causation:
when a change in one variable causes a change in another variable

4. Ex. 3 Using Technology to Find Best Fit Line
Use this table:
Find equation of best fit line. Identify correlation coefficient and tell what it means.
a is slope, b is y intercept, and r is correlation coefficient
𝑦=12𝑥+35.1
r = .979
Strong positive correlation
Closer to one the stronger it is
Steps
1. push stat button
2. hit enter on edit
3. enter x values into L1 column
Press enter each time
4. enter y values into L2 column
5. push stat again
6. arrow to the right to calc
7. push 4
8. hit enter
Duration 2
3.7
4.2
1.9
3.1
2.5
4.4
3.9
Time 60 83 84 58 72 62 85

5. Your Practice
Use the table to find equation of best fit line and correlation coefficient and interpret correlation coefficient
𝑦=−1.3𝑥+7.8
r = -.886
Strong negative correlation x -4 -2 2 4 6 8 10 y 17 7 1 5 -8

6. Ex. 4 Interpolating and Extrapolating
Using 𝑦=12𝑥+35:
Approximate the duration a time of 77 minutes
Interpolate (approximate) means to find x, so plug in for y and solve for x
77=12𝑥+35
− −35
42=12𝑥
42 12 = 12𝑥 12
3.5=𝑥
Using 𝑦=12𝑥+35:
Predict the time after an eruption lasting 5 minutes
Extrapolate (predict) means to find y, so plug in for x and solve for y 𝑦=
𝑦=60+35
𝑦=95

7. Your Practice Pg 207 number 19 don’t do letter c A. 𝑦=−.2𝑥+20
B. r = -.968, strong negative correlation
D. 22,500
E. $18,800

8. Ex. 5 Identifying Correlation and Causation
Causation: when a change in one variable causes a change in another variable
Produces a strong correlation
Correlation does NOT mean causation
Tell whether a correlation is likely in the situation. If so, tell whether there is a causal relationship.
A. time spent exercising and the number of calories burned
Positive correlation and causal
B. number of banks and the population of a city
Positive correlation, but not causal
Building more banks does not cause population to rise

9. Your Practice Time spent playing video games and grade point average
Negative correlation, causal
Number of hats you own and the size of your head
No correlation, not causal