Question

Question 1
    What is dummy variables means? And what do you understand from dummy trap?

Question 2
   In his study on the labor hours spent by the FDIC (Federal deposit insurance Corporation) on 91 bank examinations, R.J. Miller estimated the following function.
lnY=2.41+0.3674lnX1+0.2217lnx2+0.0803lnx3-0.1755D1+0.2799D2+0.5634D3-0.2572D4
     (0.55)     (0.0477)       (0.0628)      (0.0287)      (0.2905)    (0.1044)     (0.1657)     (0.0787)
R2=0.766
Where Y= FDIC examiner labor hours
            X1= Total assets of bank, x2 total number of offices in bank, x3 ratio of classified loans to total loan for bank . D1=1 if management rating was good D2=1 if management rating was fair D3=1 if management rating was satisfactory D4=1 if examination was conducted jointly with the state.
a) Interpret the results
b) Interpret the dummy variables
c) Which of the parameters from the estimated regression are statistically significant at 5% significance level?  
Question 3
Using the data in SLEEP75.RAW, we obtain the estimated equation
Sleep =3,840.83 -.163totwrk - 11.71educ - 8.70 age -.128 age2 + 87.75 male            
              (235.11)    (.018)              (5.86)        (11.21)          (.134)       (34.33)                     
N=706, R2=.123,
The variable sleep is total minutes per week spent sleeping at night, totwrk is total weekly minutes spent working, educ and age are measured in years, and male is a gender dummy.
a) All other factors being equal, is there evidence that men sleep more than women? How strong is
The evidence?
b) Is there a statistically significant tradeoff between working and sleeping? What is the estimated
Tradeoff?
c) What other regression do you need to run to test the null hypothesis that, holding other factors
Fixed, age has no effect on sleeping?

Question 4
From the data for 46 states in the United States for 1992, Baltagi obtained the following regression results:
                                              LogC= 4.3- 1.34 log P +0.17 log Y
                                                    Se=(0.91) (0.32)       (0.20)                                    R2=0.27

Where C= cigarette consumption, Packs per year
              P= real price per pack
              Y= real disposable income per capita
a. What is the elasticity of demand for cigarettes with respect to price? Is it statistically significant?
b. What is the income elasticity of demand for cigarettes? Is it statistically significant?
c. What is the overall significance of the regression? Which test do you use?

Answer 1

Sol:

1).

A dummy variable or an indicator variable is a quantative variable that represents categorical data, such as sex , race etc .

So dummy variable are dichotomous(1 or 0)quantitative variables.The regression results are easiest to interpret when dummy variables are limited to two specific values, 1 or 0. Where 1 represents the presence of a qualitative attribute, and 0 represents the absence. .

A Dummy variable trap is a situation where the attributes which are highly correlated that is the depict Multicollinearity and one variable predicts the value of others. If we use one hot encoding for handling the categorical data, then one dummy variable that is the attribute, can be predicted with the help of other dummy variables. Hence, one dummy variable is highly correlated with other dummy variables. So When we use all dummy variables for a regression model, it will lead to dummy variable trap.

2(.