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# 11 - STAT E-50 Introduction to Statistics Inferences for...

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STAT E-50 - Introduction to Statistics Inferences for Regression The fitted regression line has the equation ˆ 0 1 y = b +b x . Now we can find confidence intervals and perform hypothesis tests for the slope. The idealized regression line is y 0 1 μ = β + β x + ε where ε is the error y - μ y for each data point (x, y). ε = “epsilon” 1

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Assumptions for the model and the errors: 1. Linearity Assumption Straight Enough Condition: does the scatterplot appear linear? Check the residuals to see if they appear to be randomly scattered 2. Independence Assumption: the errors must be mutually independent Randomization Condition: the individuals are a random sample Check the residuals for patterns, trends, clumping 2
3. Equal Variance Assumption: the variability of y should be about the same for all values of x Does The Plot Thicken? Condition: Is the spread about the line nearly constant in the scatterplot? Check the residuals for any patterns 3

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