CHAPTER 5 REGRESSION Discovering Statistics Using SPSS © Andy Field 2005 Figure 4.1 Discovering Statistics Using SPSS © Andy Field 2005 Please find out the mean, variance, standard deviation of the two variables. Then, calculate the covariance, and the r and R square. Discovering Statistics Using SPSS © Andy Field 2005 We also talked about partial correlation. • Do you remember how to use SPSS to calculate this and how to interpret this? Discovering Statistics Using SPSS © Andy Field 2005 Moving beyond Correlation • Correlation is useful to tell us the relationship about two variables, but it tells us nothing about the predictive model to our data and use that model to predict values of the Dependent variable from one or more independent variables. Discovering Statistics Using SPSS © Andy Field 2005 The method of least squares • We need to find a “model” that has the least “variances” and best fit the data. • It means we need to find a straight line to “describe” our data. Discovering Statistics Using SPSS © Andy Field 2005 A straight line… 1. The slope (or gradient) of the line; and 2. The point at which the line crosses the vertical axis of the graph (known as the intercept of the line). Discovering Statistics Using SPSS © Andy Field 2005 Figure 7.1 Discovering Statistics Using SPSS © Andy Field 2005 Figure 7.2 – A Regression Line: a line that minimizes the sum of squared differences. Discovering Statistics Using SPSS © Andy Field 2005 Figure 5.3 - Goodness-of-fit: how “fit” is the line? SSm = SSr - SSt Discovering Statistics Using SPSS © Andy Field 2005 SSm • If the value of the SSm is larger, then the regression model is very different from using the mean to predict the dependent variable. • If the value of the SSm is small, then using the regression model is little better than using the mean as the model. Discovering Statistics Using SPSS © Andy Field 2005 R square • It represents the amount of variance in the outcome explianed by the SSm relative to how much variation was to explain by the SSt (mean). • Thus, R square = SSm/SSt Discovering Statistics Using SPSS © Andy Field 2005 F ratio • Is a measure of how much the model has improved the prediction of the outcome compared to the level of inaccuracy of the model. • A good model should have a large F-ratio. Discovering Statistics Using SPSS © Andy Field 2005 Class exercise – weekly records. • R square = .335, which tells us that advertising expenditure can account for 33.5% of the variation in record sales. • ANOVA test = F ratio = 99.587 • Beta = the change in the outcome associated with a unit change in the predictor = if our independent variable is increased by 1 unit, the our model predicts that 0.096 extra records will be sold. • T-test = tests the null hypothesis that the value of beta is 0: therefore, if it is significant we accept the hypothesis that the beta value is significantly different from zero and that the predictor variable contributes significantly to our ability to estimate values of the outcome. Discovering Statistics Using SPSS © Andy Field 2005 Figure 5.4 Discovering Statistics Using SPSS © Andy Field 2005 MULTIPLE REGRESSION Discovering Statistics Using SPSS © Andy Field 2005 • A logical extension of the simple regression model to situations in which there are several independent variables. • We talked about regression LINE in a simple regression model, now we are talking about a regression PLANE Discovering Statistics Using SPSS © Andy Field 2005 Figure 5.6 Discovering Statistics Using SPSS © Andy Field 2005 Methods of regression • Hierarchial (Blockwise Entry): based on early research findings • Forced Entry: all enter at once but based on previous research • Stepwise methods: exploratory Discovering Statistics Using SPSS © Andy Field 2005 Figure 7.7 Outliers – Check Cook’s distance Discovering Statistics Using SPSS © Andy Field 2005 Figure 7.9 Discovering Statistics Using SPSS © Andy Field 2005
