Question

The therm dataset contains information on survey respondents’ opinions about various public figures. These are “feeling thermometer” scores, which range from 0 (total dislike of the person) to 100 (total like). The relevant variables for this question are:

• white: a dummy variable indicating whether the respondent is white (ie, 1 for white and 0 for non-white)

• ideology: the respondent’s ideology on a scale of 1 (most liberal) to 7 (most conservative)

• obama: the respondent’s “feeling thermometer” score for Barack Obama

(a) One regression with obama as the dependent variable and white and ideology as the independent variables shows that

obama = 111.2 − 21.2 ∗ white − 8.7 ∗ ideology

What is the estimated intercept for white respondents? What about for non-white respondents?

(b) Another regression that includes a term for the interaction between white and ideology shows that

obama = 90.3+ 8.3∗white−3.0∗ideology−7.6∗(white ·ideology)

What are the estimated intercept and slope of ideology among white respondents? What about among non-white respondents? Is the relationship between ideology and Obama opinion stronger for white respondents, or non-white respondents?

Answer 1

a) The estimated regression equation is

where white: a dummy variable indicating whether the respondent is white (ie, 1 for white and 0 for non-white)

the estimated equation for white respondent can be obtained by substituting white=1 in the above equation

ans: the estimated intercept for white respondents is 90

the estimated equation for non-white respondent can be obtained by substituting white=0 in the above equation

ans: the estimated intercept for non-white respondents is 111.2

b) The estimated regression equation now is

the estimated equation for white respondent can be obtained by substituting white=1 in the above equation

ans: the estimated intercept is 98.6 and slope of ideology is -10.6 among white respondents

the estimated equation for non-white respondent can be obtained by substituting white=0 in the above equation

ans: the estimated intercept is 90.3 and slope of ideology is -3.0 among non-white respondents

The value of the slope of ideology among white respondents is -10.6. This means that for one unit increase in the respondent’s ideology (that means movement towards being conservative), decreases the "feeling thermometer" score for Barack Obama by 10.6 among the white respondents.

The value of the slope of ideology among non-white respondents is -3.0. This means that for one unit increase in the respondent’s ideology (that means movement towards being conservative), decreases the "feeling thermometer" score for Barack Obama by 3.0 among the non-white respondents.

That means the drop in the "feeling thermometer" score for one unit change in the ideology of the respondent is higher among the white respondents compared to the non-white respondents.

Hence we can say that the  relationship between ideology and Obama opinion is stronger for white respondents, in comparison to non-white respondents.