Are good looks an advantage when running for political office? This was the question of interest in an article published in the Journal of Public Economics (Feb. 2010). The researchers focused on a sample of 641 non incumbent candidates for political office in Finland. Photos of each candidate were evaluated by non-Finnish subjects; each evaluator assigned a beauty rating-measured on a scale of 1 (lowest rating) to 5 (highest rating) - to each candidate. The beauty ratings for each candidate were averaged, then the average was divided by the standard deviation for all candidates to yield a beauty index for each candidate. (A 1-unit increase in the index represents a 1-standard-deviation increase in the beauty rating.) The relative success (measured as a percentage of votes obtained) of each candidate was used as the dependent variable (y) in a regression analysis. One of the independent variables in the model was beauty index (x).
a. Write the equation of a simple linear regression relating y to x.
b. Does the y-intercept of the equation, part a, have a practical interpretation? Explain.
c. The article reported the estimated slope of the equation, part a, as 22.91. Give a practical interpretation of this value.
d. The standard error of the slope estimate was reported as 3.73. Use this information and the estimate from part c to conduct a test for a positive slope at α = .01. Give the appropriate conclusion in the words of the problem.