Chapter 9 Correlation Linear Regression Correlation n n

Chapter 9 Correlation & Linear Regression

Correlation n n The relationship between two things (x, y) x is the independent (explanatory) variable y is the dependent (response) variable

Correlation & Scatterplots n n Positive Correlation Negative Correlation Nonlinear Correlation No Correlation

Positive Correlation y x

Negative Correlation y x

Nonlinear Correlation y x

No Correlation y x

What is Linear Regression? 10 x 1 2 4 6 8 9 y 3 0 -1 -4 -7 -9 y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8 -10 What’s the equation of this line that best fits this data?

Perform a Linear Regression x 1 2 4 6 8 9 y 3 0 -1 -4 -7 -9 n Input Lists n n n n x in L 1 y in L 2 2 nd #0 “Diagnostic On” Stat “Calculate Menu” #4 “Lin. Reg(ax+b)” Enter r = -0. 99

Try Another One! n Perform a Linear Regression on the data. Find r. x y 10 y 8 -9 -6 -2 1 3 8 -5 -2 -3 0 2 4 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 -10 r =. 95 10 x

Try Another One! x y -7 8 -5 7 -2 3 0 0 1 1 3 -1 5 -6 7 -9 n Perform a Linear Regression on the data. Find r. 10 y 8 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 -6 r = -0. 98 -8 -10 4 6 8 10 x

Try Another One! x -9 -9 -7 -6 -5 -4 -3 -1 y -9 -8 -4 -7 -1 -3 -2 -1 x 0 1 2 2 3 5 7 9 y 0 -1 1 4 5 6 6 6 n Perform a Linear Regression on the data. Find r. 10 y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 -10 r =. 94 10 x