Chapter 3 Vocabulary Linear Regression

Linear Regression What is regression? Explanatory variable It is trying to find a trend for data. It could be linear regression, quadratic regression, cubic regression, etc. We are studying only linear regression in this chapter. Explanatory variable It is the “X” in the scatterplot and is the variable that attempts to “explain” or “drive” the other variable. Response variable It is the “Y” in the scatterplot and is the variable that is reacting to the other variable.

Linear regression vocab Least Squares Regression Line (LSRL) This is a type of linear trend line. There are other types of linear trend lines, such as the median-median line. This is the only linear trend line that we study in this course. The name “least squares” comes from the fact that this line minimizes the sum of the squared residuals.

Linear regression vocab Residuals: this is the observed point – the predicted point. It is the vertical distance between the line and the actual point (show example) Bivariate data: Most data with an x and a y value are graphed in a scatter plot. Residual plot: shows the values of the residuals on a plot that is easy to read. Lack of a pattern shows that the line is a good fit for the data.

Correlation coefficient “R” is the symbol for the correlation coefficient. Correlation of significance starts at .6 or -.6 and strong correlation starts at .8 or -.8. The formula is wild and done via software. The mean is in the formula and therefore is subject to the affects of outliers. Between -.6 and .6 there is considered little correlation. Correlation does not mean causation.

Coefficient of determination “R-squared” is the symbol. Uses the same math as “R” but means something completely different. It means “the percentage of variability in y due to X.” Outliers or influential points will affect greatly. The residual plot is a better measure of fit than is the value of R^2 You should memorize the catch phrase at left. Memorize the name for R-squared.