Question

Consider two models that you are to fit to a single data set involving three variables: A, B, and C.

Model 1 : A ~B

Model 2 : A ~B + C

(a) When should you say that Simpson’s Paradox is occuring?

A. When Model 2 has a lower R2 than Model 1.

B. When Model 1 has a lower R2 than Model 2.

C. When the coef. on B in Model 2 has the opposite sign to the coef. on B in Model 1.

D. When the coef. on C in Model 2 has the opposite sign to the coef. on B in Model 1.

(b) True or False: If B is uncorrelated with A, then the coefficient on B in the model A ~ B must be zero.

(c) True or False: If B is uncorrelated with A, then the coefficient on B in a model A ~ B+C must be zero.

(d) True or False: Simpson’s Paradox can occur if B is uncorrelated with C.

Answer 1

C. When the coef. on B in Model 2 has the opposite sign to the coef. on B in Model 1.

simpson paradox is said to occur when the correlation between explanatory and response variable is reversed. iethe sign of the regression slopes will be opposite.The Simpson’s Paradox may occur when there is (at least) one confounding variable (like age group ,gender etc that has not been accounted for.

for eg if there are three age groups and you are studying the effectiveness of a new medcine w. r. t the age groups. the effectivess may vary according to the age group and if the age factor is confounded then we may or may not conclude that the new medicine is ineffective, when actually is more effective on people less than age 40.

b) True, because in the regression having only one explantory variable, slope b depends on r ie

c)False, The coefficient need not be zero ie When you have more than one explanatory variable in a multiple regression, an explanatory variable uncorrelated with the response variable can have a nonzero slope because the interation of two or more explanatory variables may contribute to the variability in the response

d)False, simpson paradox has nothing to with the correlation between explanatory variables.