AP Stats: 3.3 Least-Squares Regression Line Regression Line is a straight line that describes how a response variable (y) changes as an explanatory variable (x) changes. This is a MODEL for the data.   We us the regression line to make PREDICTIONS

Least-squares regression line (LSRL) of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

Calculator: LinReg(a+bx) L1, L2, Y1 Equations of the LSRL ***SLOPE intercept Calculator: LinReg(a+bx) L1, L2, Y1

Coefficient of Determination - r2 The fraction of the variation in the values of y that is explained by least-squares regression of y on x. “we say ?% of the variation in y is explained by least-squares regression of y on x.”

Residuals – The difference between an observed value of the response variable and the value predicted by the regression line. Residual = observed y – predicted y Resid =

Residual Plot : plots the residuals on the vertical axis against the explanatory variable on the horizontal axis.       The mean of the residuals is always 0 (if not we have rounding error)

Influential An observation is Influential if removing it would markedly change the position of the regression line. Points that are outliers in the x direction are often influential.