POLI 30 Lecture Notes - Lecture 12: Squared Deviations From The Mean
Document Summary
We are looking at the relationship between two continuous variables. We know the correlation coefficient, but we also would like to know. What exactly is the relationship between x and y. Regression will let us answer all these questions. We use a straight line to summarize these relationships. The line tells us the nature of the relationship. The line also allows us to predict new observations. Finally, regression and inference let us distinguish between real and random relationships. We pick the line that minimizes the sum of vertical squared deviations from the line. To find the right line you use calculus to minimize the sum of squared deviations from the line: summation( yi - (a + bxi)) ^2. A = ybar - b * xbar. This is the formula for least squares regression line. We call it old because it minimizes the squared distances from the line. B: a one unit increase in x produces a b-unit increase in y.
