1. CHAPTER 5
REGRESSION
Discovering Statistics Using SPSS

2. Figure 4.1
Discovering Statistics Using SPSS

3. Then, calculate the covariance, and the r and R square.
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

4. 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

5. 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

6. 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

7. A straight line… The slope (or gradient) of the line; and
The point at which the line crosses the vertical axis of the graph (known as the intercept of the line).
Discovering Statistics Using SPSS

8. Figure 7.1
Discovering Statistics Using SPSS

9. Figure 7.2 – A Regression Line: a line that minimizes the sum of squared differences.
Discovering Statistics Using SPSS

10. Figure 5.3 - Goodness-of-fit: how “fit” is the line?
SSm = SSr - SSt
Discovering Statistics Using SPSS

11. 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

12. 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

13. 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

14. 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 =
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 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

15. Figure 5.4
Discovering Statistics Using SPSS

16. Multiple regression
Discovering Statistics Using SPSS

17. 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

18. Figure 5.6
Discovering Statistics Using SPSS

19. 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

20. Figure 7.7 Outliers – Check Cook’s distance
Discovering Statistics Using SPSS

21. Figure 7.9
Discovering Statistics Using SPSS