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Regressionhw

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User Generated
Subject
Statistics
School
George Washington University
Type
Homework
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Part 1: Working with Dummy Variables
Instructions: You must show all work and/or provide a full explanation for the following
problems. You should use R or other software for plots.
1. (based on text p. 337: 8.13) Consider a regression model π‘Œ = 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 + πœ€, where 𝑋1 is
a numerical variable and 𝑋2 is a dummy variable. Plot the response functions (the graphs of 𝐸(π‘Œ)
as a function of 𝑋1 for different values of 𝑋2), if 𝛽0=25, 𝛽1=0.2, and 𝛽2=βˆ’12.
E{Y} = 25 + 0.2X
1
- 12X
2
When X
2
= 0, the response function is:
E{Y| X
2
= 0} = 25 + 0.2X
1

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When X
2
= 1, the response function is:
E{Y| X
2
= 1} = 25 + 0.2X
1
-12 = 13 + 0.2X
1
2. Continue the previous exercise. Sketch the response curves for the model with interaction, π‘Œ =
𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 +𝛽3𝑋1𝑋2+ πœ€, given that 𝛽3=βˆ’0.2.
E{Y} = 25 + 0.2X
1
- 12X
2
- 0.2X
1
X
2

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Part 1: Working with Dummy Variables Instructions: You must show all work and/or provide a full explanation for the following problems. You should use R or other software for plots. 1. (based on text p. 337: 8.13) Consider a regression model π‘Œ = 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 + πœ€, where 𝑋1 is a numerical variable and 𝑋2 is a dummy variable. Plot the response functions (the graphs of 𝐸(π‘Œ) as a function of 𝑋1 for different values of 𝑋2), if 𝛽0=25, 𝛽1=0.2, and 𝛽2=βˆ’12. E{Y} = 25 + 0.2X1 - 12X2 When X2 = 0, the response function is: E{Y| X2 = 0} = 25 + 0.2X1 When X2 = 1, the response function is: E{Y| X2 = 1} = 25 + 0.2X1 -12 = 13 + 0.2X1 2. Continue the previous exercise. Sketch the response curves for the model with interaction, π‘Œ = 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 +𝛽3𝑋1𝑋2+ πœ€, given that 𝛽3=βˆ’0.2. E{Y} = 25 + 0.2X1 - 12X2 - 0.2X1 X2 When X2 = 0, the response function is: E{Y| X2 = 0} = 25 + 0.2X1 When X2 = 1, the response function is: E{Y| X2 = 1} = 25 + 0.2X1 -12 - 0.2X1 = 13 3. (based on text p.340: 8.34) In a regression study, three types of banks were involved, namely, (1) commercial, (2) mutual savings, and (3) savings and loan. Consider the following dummy variables for the type of bank: a) Develop the first-order linear regression model (with no interactions) for relating last year’s profit or loss (π‘Œ ) to the size of the bank (𝑋1) and type of bank (𝑋2,𝑋3). π‘Œ = 𝛽0 + 𝛽1𝑋1 + 𝛽2? ...
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