# Statistics Ch 5

 The flashcards below were created by user firefly501 on FreezingBlue Flashcards. Regression line a straight line that describes how a response variable y changes as an explanatory variable x changes. One variable explains or predicts the other.May be used to predict the value of y for a given value of x. Least-squares regression line: the unique line such that the sum of the squared vertical(y) distances between the data points and the line is the smallest possible. Facts about least-squares regression: 1. The distinction between explanatory and response variables is essential in regression.2. There is a close connection between correlation and the slope of the least-squares line.3. The least-squares regression line always passes through the point ( x , y )4. The correlation r describes the strength of a straight-line relationship. The square of the correlation, r2, is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x. Equation of least-squares regression line: Coefficient of determination, r2 r2: the fraction of the variance in y (vertical scatter from the regression line) that can be explained by changes in x. Residuals dist. ( y - yˆ) = residual Residual plots Residuals are the distances between y-observed and y-predicted. We plot them in a residual plot.If residuals are scattered randomly around 0, chances are your data fit a linear model, were normally distributed, and you didn’t have outliers.The x-axis in a residual plot is the same as on the scatterplot.The line on both plots is the regression line. Outlier: An observation that lies outside the overall pattern of observations. Influential individual An observation that markedly changes the regression if removed.This is often an outlier on the x-axis. Interpolation Making predictions The equation of the least-squares regression allows you to predict y for any x within therange studied. This is called interpolating. lurking variable is a variable not included in the study design that does have an effecton the variables studied.It can falsely suggest a relationship. Confounded variables Two variables are confounded when their effects on a response variable cannot bedistinguished from each other. The confounded variables may be either explanatoryvariables or lurking variables. Extrapolation is the use of a regression line for predictions outside the range of x values used to obtain the line. Authorfirefly501 ID137598 Card SetStatistics Ch 5 DescriptionRegression Relationship between two variables Updated2012-02-27T16:01:28Z Show Answers