STATS 1000 / STATS 1004 / STATS 1504 Statistical Practice 1 Practical Week 11 Multiple Linear regression 2015 Practical Outline In this practical, we will • Get multiple scatter-plots. • Recap how to look at correlations between variables. • Look at how to perform multiple linear regression in SPSS. Part I – Learning about SPSS The dataset we will use is the cheese.sav. This is described in Appendix A. Load this dataset into SPSS. It should look like this: 1 Scatter-plot matrices To look at the relationship between the response variable taste and the predictor variables acetic, H2s and lactic, we are going to produce a scatter-plot matrix. • Select Graphs > Legacy Dialogs > Scatter/Dot... • Select the Matrix Scatter, then click Define • Move taste, acetic, H2S and lactic into Matrix Variables: 2 • Click OK Question Describe the relationship between taste and the predictors Correlation between response variable and the predictor variables Next we will example the correlation between the response variable taste and the predictor variables acetic, H2S, and lactic. This is done thus: • Select Analyze > Correlate > Bivariate... 3 • Put taste, acetic, H2S, lactic into Variables: • Click OK 4 Question Which predictor variables have a statistically significant correlation with taste? Fitting a multiple linear regression model. To fit the multiple linear regression with taste as the response variable and acetic, H2S, and lactic as predictor variables do the following steps: • Select Analyze > Regression > Linear • Put taste into Dependent: • Put acetic, H2S, and lactic into Independent(s): • Click OK This should give the following output: 5 Question Can any of the predictors be removed from the model? Using a P-value cutoff of 5% find the smallest model. Part II – Exercises There are no exercises this week, please feel free to work on the assignments. Part III – Appendix A Cheese dataset As cheddar cheese matures, a variety of chemical processes take place. The taste of matured cheddar is related to the concentration of several chemicals in the final product. In a study of cheddar cheese from the LaTobe Valley of Victoria, Australia, samples of cheese were analysed for their chemical composition and were subjected to taste tests. The variable Case is used to number the observations from 1 to 30. taste is the response variable of interest. The taste scores were obtained by combining the scores from several tasters. Three of the chemicals whose concentration were measured were acetic acid, hydrogen sulphide, and lactic acid. For acetic acid and hydrogen sulphide (natural) log transforms were taken. Thus, the explanatory variables are the transformed concentrations of acetic acid (acetic) and hydrogen sulphide (H2S), and the untransformed concentration of lactic acid (lactic). 6

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