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Analysis Tools (TPTM6496). Matthew Beck matthewb@itls.usyd.edu.au Consultation by appointment. Introduction to Regression. Tutorial Outline: What is Regression? Regression in SPSS Assumptions of Regression Testing Assumptions. Introduction to Regression. What is regression?

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## Analysis Tools (TPTM6496)

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**Analysis Tools (TPTM6496)**Matthew Beck matthewb@itls.usyd.edu.au Consultation by appointment**Introduction to Regression**• Tutorial Outline: • What is Regression? • Regression in SPSS • Assumptions of Regression • Testing Assumptions**Introduction to Regression**• What is regression? • It allows us to measure the amount of variation in one dependent variable, using the variation in a number of known independent variables. • It fits a straight line to best estimate the data. • It is a predictive tool.**Introduction to Regression**• An example: • Can we explain variations in student grades by examining how many hours they study? Dependent Variable Independent Variable**Introduction to Regression**(y) Grade What does this line remind you of? 80 70 60 50 40 30 20 Gradient formula? y = mx + b “m” measures the gradient, i.e., in what way does y change when x changes? (x) Hours of Study 1 2 3 4 5**Introduction to Regression**• Looking at the math: • We want to solve: grade = b + m(study) • Or in other words: + e 0 + 1 Y = X**Introduction to Regression**• The formulas: = = 10.06 = 20.65**Introduction to Regression**• Our regression model becomes: • We can use this model to make predictions about peoples grades! Grade = 20.65 + 10.06(hours of study)**Introduction to Regression**• We can see how regression works. • We know what it does. • What if the model was more complicated? Sales = 0 + 1($ ad) + 2(# staff) + 3(colour) • This is why we use SPSS!**Introduction to Regression**• Open the Program. • Enter the “grades & study” data. • Analyze – Regression – Linear • See how much easier that is? • Open up the Sofa-World dataset.**Introduction to Regression**• Assumption 1 - Linear Relationship: • Regression can only model a straight line relationship between the dependent and independent variable(s). • Scatterplot: • Sales vs. Price • Sales vs. Parts • What about Sales vs. Colour – why is colour different?**Introduction to Regression**• Examples of nonlinear relationships:**Introduction to Regression**• What about this?**Introduction to Regression**• Assumption 2: No Multicollinearity: • Independent variables cannot be correlated with each other. • Scatterplot: • Price vs. Parts • What do you see? • What should we see?**Introduction to Regression**• Assumption 3: Homoscedaticity: • The variance of the error term must be constant.**Introduction to Regression**• Assumption 4: Normal error term: • The error term must follow a normal distribution (i.e., follow a bell curve):**Introduction to Regression**• Check for linear relationship and multicollinearity before analysis. • Check for homoscedaticity and normality using commands in regression function. Analyze – Regression – Linear – Plots • Graph ZRESID(ual) vs ZPRED(icted). • Select P-P plot and Histogram**Introduction to Regression**• Linearity of Relationship • No Multicollinearity • Homoscedaticity • Normal Distribution • Independence of the variance term**Introduction to Regression**• Run the regression using price and colour as the dependent variables. • Lets interpret some output. • Write out the regression model. • How can we use this model? • Remember, the important component of data analysis is providing relevant information.**Introduction to Regression**• Significance testing: • p-value/sig-value = probability of the result occuring, given the null is true. • Basically, the smaller the value, the more unlikely it is the result actually occurred. • The more unlikely the result is, the more we pay attention to it…it is a special result…it is a significant result. • Normally we set , or LOS = 0.05. • If sig < 0.05 we have a significant result (we reject the null).

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