SWBAT: Calculate and interpret the equation of the least-squares regression line Do Now: If data set A of (x, y) data has correlation r = 0.65, and a second data set B has correlation r = –0.65, then (a) the points in A fall closer to a linear pattern than the points in B. (b) the points in B fall closer to a linear pattern than the points in A. (c) A and B are similar in the extent to which they display a linear pattern. (d) you can’t tell which data set displays a stronger linear pattern without seeing the scatterplots. (e) a mistake has been made—r cannot be negative.

SWBAT: Calculate and interpret the equation of the least-squares regression line Regression A regression line is a line that describes how a response variable (y) changes as an explanatory variable (x) changes Regression line predicts the value of y for a given value of x. * Predicting outside the interval of the explanatory variable (x) is called Extrapolation - Often not accurate ŷ = a + bx ŷ - (read “y hat”) is the predicted value of the response variable y for a given value of the explanatory variable x. b is the slope, the amount by which y is predicted to change when x increases by one unit. a is the y intercept (the predicted value of y when x = 0).

SWBAT: Calculate and interpret the equation of the least-squares regression line Residual A residual is the difference between an observed value of the response variable (y) and the value predicted by the regression line. Least-squares regression line The least-squares regression line of y on x is the line that makes the sum of the squared residuals as small as possible

SWBAT: Calculate and interpret the equation of the least-squares regression line Example: (a)Calculate the Least-Squares Regression Equation: (b)Predict the backpack weight of a hiker who weighs 200 lbs. Is this a good prediction to use? Why or why not? (c)Find and interpret the residual for the hiker who weighed 187 pounds.