t-tests
Problem
Consider the Mortality data at http://www.oswego.edu/~kane/econometrics/data.htm . Regression result:
MORT = Total Mortality Rate per 100,000 Population
INCC = Per-Capita Income by State, in Dollars
POV = Proportion of Families Living Below the Poverty Line by State
ALCC = Per-Capita Consumption of Alcohol by State, in Gallons
TOBC = Per-Capita Consumption of Cigarettes by State, in Packs
PHYS = Physicians per 100,000 Population
AGED = Proportion of Population over the Age of 65
- Check the signs of the coefficients. Do they make sense to you?
- Test and interpret \(H_0:β_{income}=0\) \(\left( α=0.05 \right)\)
- Test and interpret \(H_0:β_{tobacco}=0\) \(\left( α=0.01 \right)\)
Solution
- INCC is not significant (see b). POV is positive, the higher the proportion of families living below the poverty line, the higher the mortality rate. That makes sense. More alcohol tend to reduce mortality – not sure about this. Tobacco is super significant in increasing mortality – definitely expected. More physicians tend to increase mortality – that’s a bit scary… Aged also tend to increase mortality.
- T-value is -142/90 = 1.58 which is clearly below the critical value. Do not reject. It is possible that \(β_{income}=0\) at \(α=0.05\) .
- T-value is 1.69/0.30 = 5.61. The critical value at 1% is 2.69 so reject even at this level. Tobacco is the most significant variable explaining mortality.