10. Multiple regression introduction

10. Multiple regression introduction - Multiple Regression...

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Multiple Regression Model In many applications in business and economics, the dependent variable Y is predicted on the basis of several independent variables X 1 , X 2 , X 3 ,…. X k . For example, Y House Price(\$000s), could be forecast based on X 1 = Floor space (square feet), X 2 = Number of floors, X 3 = Number of bedrooms, X 4 = Number of bathrooms.

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Multiple (Linear) Regression Model Interpretation of this model: β 1 is the expected increase in Y when X 1 is increased by one unit, when the values of all the other X i ’s remain fixed ( ceteris paribus) . Similar interpretations for the other β i ’s. 0 1 1 2 2 k k β X β X ... β X e = + + + + +
“Good” independent (predictor) variable, X Should be related to the dependent variable Should not be too highly related to other independent variables This may be checked through correlation matrix

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HOUSEPRICE SQFT NUM FLRSBDRM S BATHS 69 6 1 2 1 11.5 8 1 2 1 118.5 10 1 2 2 104 11 1 3 2 116.5 10 1 3 2 121.5 10 1 3 2 125 11 1 3 2 128 15 2 3 2.5 129.9 13 1 3 1.7 133 13 2 3 2.5 135 13 2 3 2.5 137.5 15 2 3 2.5 139.9 13 1 3 2 143.9 14 2 3 2.5 147.9 17 2 3 2.5 154.9 15 2 3 2.5 160 19 2 3 2 169 15 1 3 2 169.9
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10. Multiple regression introduction - Multiple Regression...

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