9.2. Least-Squares Regression http://www.ck12.org
9.2 Least-Squares Regression
Learning Objectives
- Calculate and graph a regression line.
- Predict values using bivariate data plotted on a scatterplot.
- Understand outliers and influential points.
- Perform transformations to achieve linearity.
- Calculate residuals and understand the least-squares property and its relation to the regression equation.
- Plot residuals and test for linearity.
Introduction
In the last section we learned about the concept of correlation, which we defined as the measure of the linear
relationship between two variables. As a reminder, when we have a strong positive correlation, we can expect that
if the score on one variable is high, the score on the other variable will also most likely be high. With correlation,
we are able to roughlypredictthe score of one variable when we have the other. Prediction is simply the process of
estimating scores of one variable based on the scores of another variable.
In the previous section we illustrated the concept of correlation through scatterplot graphs. We saw that when
variables were correlated, the points on this graph tended to follow a straight line. If we could draw this straight
line it, in theory, would represent the change in one variable associated with the other. This line is called theleast
squaresor thelinear regression line(see figure below).