Submitted by: Submitted by lisijia08013
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Category: Science and Technology
Date Submitted: 04/25/2013 02:20 PM
Topics in Multiple Regression
In this set of notes we present different extensions to the regular multiple regression model formulated by y=β0+β1x1+β2x2+…+βk+ε. First we discuss the dummy variable that deals with categorical (qualitative) data and then we’ll add the interaction term; finally we’ll discuss non linear regression models
Regression with Categorical Data
The dummy variable is a mathematical tool that makes it possible to include non-numerical information in the regression model. This makes the model more useful in decision making setting, where data may or may not belong to a certain category.
Value | Size(1000ft2) | Fireplace |
84.4 | 2 | Yes |
77.4 | 1.71 | No |
75.7 | 1.45 | No |
85.9 | 1.76 | Yes |
79.1 | 1.93 | No |
70.4 | 1.2 | Yes |
75.8 | 1.55 | Yes |
85.9 | 1.93 | Yes |
78.5 | 1.59 | Yes |
79.2 | 1.5 | Yes |
86.7 | 1.9 | Yes |
79.3 | 1.39 | Yes |
74.5 | 1.54 | No |
83.8 | 1.89 | Yes |
76.8 | 1.59 | No |
Example 1
One would like to know the effects on assessed house value of the house size, and whether or not there is a fireplace in the house. Data from a sample of 15 houses was recorded and is provided below:
The independent variable Size is quantitative (ft2), but the variable Fireplace is qualitative (Yes, No). We define a new variable “FirePlace” and let it have the value 1 when there is a fireplace and 0 when there is none. The data set becomes:
Value | Size(1000ft2) | Fireplace |
84.4 | 2 | 1 |
77.4 | 1.71 | 0 |
75.7 | 1.45 | 0 |
85.9 | 1.76 | 1 |
79.1 | 1.93 | 0 |
70.4 | 1.2 | 1 |
75.8 | 1.55 | 1 |
85.9 | 1.93 | 1 |
78.5 | 1.59 | 1 |
79.2 | 1.5 | 1 |
86.7 | 1.9 | 1 |
79.3 | 1.39 | 1 |
74.5 | 1.54 | 0 |
83.8 | 1.89 | 1 |
76.8 | 1.59 | 0 |
Now we can formulate a multiple regression model of the form:
y=β0+β1Size+β2FirePlace+ε
Price
0
0 + 2
The house value for a house with a fireplace is described by the equation
Value=β0+β1Size+β21+ε which reduces to...