slide11 - Introduction What does it mean when there is a...

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1 Introduction What does it mean when there is a strong positive correlation between x and y ? Regression analysis aims to find a precise formula to relate the movements of y to those of x The use of regression requires a good deal of thought and a good dose of skepticism 2 Example: Sales vs. Advertising Advertising (mil.$) Sales (mil.$) 1.2 120 1.6 190 1.8 260 2.2 260 2.6 300 3.1 290 3.4 330 3.6 330 4.0 340 4.2 310
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3 Example: Sales vs. Advertising 0 50 100 150 200 250 300 350 400 0 1 2 3 4 5 4 Example: Sales vs. Advertising It is believed that sales, S , are tied to advertising, A , by a simple linear equation: What do β 0 and β 1 represent? How can we find β 0 and β 1 ? A S 1 0 β β + =
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5 Sales vs. Advertising The linear relation is usually not exact. A more realistic model: Where β 0 and β 1 are regression coefficients. i i 1 0 i A S ε β β + + = 6 Measurement Error Properties of distribution A mean of zero Symmetry around zero An assignment of greater probability to small errors than to larger ones Errors are assumed to be: Independent Have same variance (
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