Multiple Regression
Essay by Paul • May 7, 2012 • Essay • 451 Words (2 Pages) • 1,679 Views
Introduction to Multiple Regression
* Real estate example
o Predict sales price of home from sqft (R2=26%) or distance from downtown (R2=37%)
o If combine two predictor variables the new R2 ≠ 26% + 37% because sqft is related to distance from downtown
o Instead, we will use multiple regression
* Multiple regression
o Extension of simple regression that allows us to analyze the relationship between multiple x variables (IV) and a y variable (DV)
o We will have to be careful about relationships between x variables
o Won't use scatterplots as much in multiple regression
Adapting Basic Concepts
* Format of equation very similar to simple regression
o Add more x variables sample equation: y = a + b1x1 + b2x2 + ...+ bkxk
o True population equation y = α + β1x1 + β2x2 + ... + βkxk + error
* Note that the coefficient is different for distance from simple and multiple regression analyses
o For simple regression: the coefficient is the change in y (price) due to one unit change in x (distance) ["gross" effect]
o For multiple regression: the coefficient is the change in y (price) due to one unit change in x (distance) controlling for other x variables (i.e., the houses have the same sqft) ["net" effect]
o Note in this example, distance has a negative effect on price (because this increases commuting time) but houses farther away tend to be bigger (the correlation between the x variables) and bigger houses tend to cost more--so, multiple regression has to balance these two predictor variables
* 4 steps to interpreting coefficients:
o Look at p-value to see if x variable (IV) coefficient is significant
o Check the sign of the coefficient to see if makes sense given your understanding of the situation
o Look at the magnitude of the coefficient to understand the structural relationship with the dependent variable
o Note which other x variables are included in the regression so you can interpret the coefficient as an appropriate gross or net effect
* gives you instructions on how to conduct multiple regression in Excel
* Residual analysis
o Residual = actual value (y) - predicted value (y hat) (same
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