PS296 Chapter Notes - Chapter 10: Squared Deviations From The Mean
Stats Chapter 10:
The Regression Line/Equation:
ŷ = bX + a
ŷ = the predicted value of Y (yhat)
b = the slope of the regression line (the amount of difference in Y associated with a one unit difference
in X)
a = the intercept (the predicted value of Y when X = 0
X is simply the value of the predictor variable
-the hat on the Y indicates that the values we are searching for are predicted values, not recorded values
Errors of Prediction:
-Y-ŷ deviations
-y – ŷ is an error of prediction called the residual
-we want to find the line (the set of ŷs) the minimizes the sum of the squared errors Σ(y – ŷ)²
-the fact that we are minimizing the squares of the residual gives our approach its name; least squares
regression
To find B:
b = covxy
Document Summary
= the predicted value of y (yhat) = the slope of the regression line (the amount of difference in y associated with a one unit difference in x) a = the intercept (the predicted value of y when x = 0. X is simply the value of the predictor variable. The hat on the y indicates that the values we are searching for are predicted values, not recorded values. Y is an error of prediction called the residual. We want to find the line (the set of s) the minimizes the sum of the squared errors (y ) . The fact that we are minimizing the squares of the residual gives our approach its name; least squares regression. = covxy s x (the variance of x, ex the sd squared) To find a: a = bx (the average of y values slope(x average) Need to solve for b first to find a.
