4.5 Analyzing Lines of Fit

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

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

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

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

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 −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=12 5 +35 𝑦=60+35 𝑦=95

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

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

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