Chapter 8 – Correlation and regression. After studying this chapter you will be able to understand: Define and interpret a scatter plot, calculate and interpret a sample covariance, calculate and interpret a sample correlation coefficient, explain how outliers can affect correlations,. | Correlation and regression 1 Scatter plots A scatter plot is a graph that shows the relationship between the observations for two data series in two dimensions. Scatter plots are formed by using the data from two different series to plot coordinates along the x- and y-axis, where one element of the data series forms the x-coordinate and the other the y-coordinate. 2 Linear Nonlinear LOS: Define and interpret a scatter plot. Page 281 Visual inspection of a scatter plot, although not sufficient to demonstrate a statistical relationship, is often a starting point for examining data in order to assess whether there appears to be an underlying relationship. The graphs in the slide depict a basic scatter plot, one with a likely linear relationship and one with a curvilinear relationship. 2 Sample covariance Recall that covariance is the weighted average of the cross-product of each variable’s departure from its mean. Sample covariance is calculated by using the same process as sample . | Correlation and regression 1 Scatter plots A scatter plot is a graph that shows the relationship between the observations for two data series in two dimensions. Scatter plots are formed by using the data from two different series to plot coordinates along the x- and y-axis, where one element of the data series forms the x-coordinate and the other the y-coordinate. 2 Linear Nonlinear LOS: Define and interpret a scatter plot. Page 281 Visual inspection of a scatter plot, although not sufficient to demonstrate a statistical relationship, is often a starting point for examining data in order to assess whether there appears to be an underlying relationship. The graphs in the slide depict a basic scatter plot, one with a likely linear relationship and one with a curvilinear relationship. 2 Sample covariance Recall that covariance is the weighted average of the cross-product of each variable’s departure from its mean. Sample covariance is calculated by using the same process as sample variance; however, rather than squaring the deviation of each observation from its mean, we take the product of two different variables’ deviations from their respective means. 3 LOS: Calculate and interpret a sample covariance. Page 284 Point out that covariance is covered in its probabilistic form in Chapter 4, and that this is just the sample analog wherein we have data from the past instead of a stated probability distribution. 3 Sample covariance Focus On: Calculations Lending rates and current borrower burden are generally believed to be related. The following data cover the debt-to-income ratio for 10 borrowers and the interest rate they are being charged on five-year loans. What is the sample covariance between loan rate (Y) and debt-to-income ratio (X)? 4 Client Y X Y-Yhat X-Xhat Product 1 2 – – 3 – – 4 – – 5 – – 6 .
