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

Correlation and Lines of Best Fit Unit 8 - Statistics

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.

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)

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!

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

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.

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

Practice Modeling y = 2.04x-2.36

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