Tax expert Bob Erikson is interested in the reliance of state governments on “sin taxes”—taxes on the purchase of alcohol and tobacco and on gambling. The dependent variable is the percentage of state revenue that is raised from sin taxes. Three research hypotheses guide Bob’s analysis. First, Bob believes that Catholics are generally “good-time” people who drink, smoke, and play bingo a lot; X1 is the percentage of the state population who are Catholic. Second, Bob notes that Republicans seem less concerned than Democrats do that sin taxes might be regressive; X2 is the percentage of the state legislature who are Republicans. Third, Bob suspects that sin taxes could be used to hold down the level of property taxes; X3 is the per-capita property tax in thousands of dollars. A regression program produces the following results:
 = .54 + .23X1 + .11X2 - 1.41X3
sb1 = .04 sb2 = .087 sb3 = .15 Sy|x = .74
R2 = .74 Adj. R2 = .71
(a) Interpret the slopes, intercept, and R2.
(b) What are the research hypotheses? Evaluate these hypotheses.
(c) Michigan has 20% Catholic constituents, 47% Republicans in the state legislature, and a property tax of $ 2.5 per thousand. What is your best guess as to the sin tax rate in Michigan?
(d) The actual sin tax rate in Michigan is 16.1%. What would you conclude about that?