Question: In the next step we shall focus on how to explain public support for President Obama among American citizens. We have a very simple research question – the feeling towards the President differs among different races and is also related to the family income of the individuals. We expect Caucasians to be more negative towards President Obama. Furthermore, we believe that the support for the President is stronger among the lower income brackets. Our dependent variable is a so called feeling thermometer. The feeling thermometer measures the respondent’s attitudes towards the President on a scale ranging from 0 to 100 where 0 means no support and 100 full support. We also have two independent variables: race and income. Race is measured on a nominal scale with four categories: 1 equals Caucasian; 2 equals African-American; 3 equals Hispanic; and 4 equals other. Family income is measured as annual family income in thousands of US dollars. The following results are based on the August 2010 opinion poll (fabricated data).

First, we run two separate bivariate regression analyses employing race and family income as independent variables and the feeling thermometer as the dependent variable. To estimate the influence of race we have recoded the nominal variable into four dummy variables. In the analysis we have left out the dummy for Caucasians. That is, Caucasians is the reference category. The results of the two bivariate analyses are presented in tables 1 and 2 below.

Intercept 45.24 13.45 < 0.01

African-American 12.29 4.58 < 0.01

Hispanic 6.67 2.31 0.02

n 1805

Note: The critical values for t at the 90% confidence level are ±1.65. The critical values for t at the 95% confidence level are ±1.96. The critical values for t at the 99% confidence level are ±2.58.

Intercept 73.24 11.24 < 0.22

n 1805

Note: The critical values for t at the 90% confidence level are ±1.65. The critical values for t at the 95% confidence level are ±1.96. The critical values for t at the 99% confidence level are ±2.58.

(a) Are the two hypotheses supported by the results?

Next, we include all the variables in the same model and get the following results.

Intercept 74.59 12.67 < 0.01

African-American 2.96 1.72 0.08

Hispanic 0.45 0.58 0.56

n 1805

Note: The critical values for t at the 90% confidence level are ±1.65. The critical values for t at the 95% confidence level are ±1.96. The critical values for t at the 99% confidence level are ±2.58.

(b) Write of the prediction equation.

(c) According to the results in Table 3, what is the expected value on the feeling thermometer towards President Obama for an African-American with a family income equal to 70 000 US dollars

(d) What happened to the original, bivariate relationship between race and support for President Obama when controlling for family income? Discuss in relation to the four causal criteria.

(e) What does the R-square statistic tell us? What does the standard error of regression statistic tell us? Which measure of goodness of fit do you prefer in this case? To give a substantive interpretation of the fit of the model it might be good to know that the univariate standard deviation of the feeling thermometer is equal to 9.149.