© Andy Field 2005Discovering Statistics Using SPSS CHAPTER 5 REGRESSION

© Andy Field 2005Discovering Statistics Using SPSS

CHAPTER 5

REGRESSION


Figure 4.1

© 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?


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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.


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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.


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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).



Figure 7.1


Figure 7.2 – A Regression Line: a line that minimizes the sum of squared differences.


Figure 5.3 - Goodness-of-fit: how “fit” is the line?

SSm = SSr - SSt

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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.


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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


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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.


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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.



Figure 5.4

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MULTIPLE REGRESSION


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• 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



Figure 5.6

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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



Figure 7.7 Outliers – Check Cook’s distance


Figure 7.9

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© Andy Field 2005Discovering Statistics Using SPSS CHAPTER 5 REGRESSION