Please write down the detail process. Thanks. Question 4. You want to study the

Question

Please write down the detail process. Thanks.

Question 4. You want to study the relationship between hourly wages (Y) and marital status and education level. You define the dummy variable M, = 1 if person i is married, Mi = 0 if i is single. You also define Ci = 1 if person i graduated from college, Ci = 0 if not. You estimate the following regression with an interaction term a) Using the regression results, calculate average wages for the four following groups: i) Single individuals who didn't graduate from college, i) Married individuals who didn't graduate from college, iii) Single college graduates, iv) Married college graduates. b) Suppose that every married person in the sample is a college graduate. Explain why that would generate perfect multicollinearity between regressors.

Explanation / Answer

Here the regression model is

Yi^ = 13 + 4Mi+ 3Ci+ 1 (Mi X Ci )

(a) SO here there are lot of combinations are there:

(i) Single individuals doesn't;t graduated from college so here M = 0 C = 0

so wages (M= 0, C=0) = 13 + 4 * 0 + 3 * 0 + 1 * (0 * 0 ) = 13

(ii) Married but no graduate

Wages (M= 1, C=0) = 13 + 4 * 1 + 3 * 0 + 1 * (1 * 0) = 17

(iii) Graduate but single

Wages (M= 0, C =1) = 13 + 4 * 0 + 3 * 1 + 1 * (0 * 1 ) =16

(iv) Graduate and married both

Wages( M=1 , C =1) = 13 + 4 * 1 + 3 * 1 + 1 * (1 * 1) = 21

(b) Here if every married person in the sample is a college graduate that makes for every M= 1 ; C = 1

Here there will be no case of married and Graduate and not married.  We have perfect multicollinearity if, for example as in the equation above, the correlation between two independent variables is equal to 1 or 1.

SO here we can see that C = M which makes it perfect multi collinear relation. Here we can change our model to

C = M (for M = 1)

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