PS296 Lecture Notes - Lecture 10: Linear Regression, Total Variation
Regression:
-regression is the prediction of one variable based on the knowledge of one or more other
variables
-allows us to examine how differences in one variable (x) relate to differences in another
variable (y)
Regression line = ŷ = bX + a
ŷ = predicted value of y
b = slope of the regression line, the amount of change in Y associated with a 1 unit change in X
X = any value of x, predictor variable
a = y intercept, the predicted value of Y when X = 0
What is the difference between correlation and regression?
-the correlation coefficient (Pearson r) represents the degree to which two variables are related
-the regression coefficient (ex slope, intercept) represents the magnitude of change in one
variable compared with the other variable
-we often refer to one variable as the predictor variable (x) and the other variable as the
outcome variable (y)
r² = variation in y explained by x
total variation in y
r² = coefficient of determination
Document Summary
Regression is the prediction of one variable based on the knowledge of one or more other variables. Allows us to examine how differences in one variable (x) relate to differences in another variable (y) Regression line = = bx + a. = slope of the regression line, the amount of change in y associated with a 1 unit change in x. X = any value of x, predictor variable a = y intercept, the predicted value of y when x = 0. The correlation coefficient (pearson r) represents the degree to which two variables are related. The regression coefficient (ex slope, intercept) represents the magnitude of change in one variable compared with the other variable. We often refer to one variable as the predictor variable (x) and the other variable as the outcome variable (y) r = variation in y explained by x total variation in y r = coefficient of determination.
