Here was the hw question: \"Suppose you were interested in the effect of income
ID: 3065289 • Letter: H
Question
Here was the hw question: "Suppose you were interested in the effect of income on health. If we reran model 1 above and called it model 2 and you added a variable called "Smoking" which measures the number of cigarettes person i smokes per day and the coefficient on INCOME changes from -0.172298 to -7.3 (assume, for simplicity, that the standard errors stay the same). What does that mean about model 1 (relative to model 2)? " The whole equation was OVERALL HEALTH SCORE = .45 Illness + .15 DAYS Reduced Activity + .028 Prescriptions Used + .013 Nonprescription medicine used - 0.17 Income ($000's)
Is there more to the answer other than model 2 has a greater impact on OVERALL HEALTH SCORE than model 1? Does the fact that the standard errors stay the same mean anything important between the two models? How do I tell if this change in income coefficient was significant?
Explanation / Answer
In model 2, after adding the "Smoking" the regression coefficient of "INCOME" decreased. It means there may be some effects which is correlated with "Health".
Yes obviously. Adding more variables, we get more value of R2, which imply this model is at least as effcient as the model 1, may be better than model 1.
Yes, although the standard error same, still adding more variables includes more interaction effects which may be important. Like there is high chance of more income persons smoke more than the lower income persons. So, there is a differece, which you also can look upon as multicolinearity.
You can perform a test, where null hypothesis is "the regression coefficient is equal to zero" against the alternative is "not equal to zero". After performing a test you will find the p-value and if it is less than the desired level of significance then you can say that there is an significant effect of that variable. If p-value is greater than the level of significance then there is no effect of the variable and you can omit the variable from the model and reconstruct the model again.