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 lineRegression

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

ResidualA residual is the difference between an observed value of the response variable (y) and the value predicted by the regression line.

Least-squares regression lineThe 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 lineExample:

(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.