There is a wide disparity between education systems across the world. Suppose we have a dataset for 42 countries. The variable X is the average years of formal education for a person in a country, and Y is the per capita income (in thousands of dollars) in that country. We find a positive relationship between the two variables. Additionally, our regression shows the following results:
Xbar=10; ybar=55; E(Xi -Xbar)^2=20; E(Y^ -Ybar)^2=200; r=0.54; n=42; S(var)=1.450
a. According to the regression results above, what percentage of the variation in income is explained by the education level?
b. What is the value of b1 in the regression Y=b0+b1X? (Hint: what is SSR and how is that related to b1?)
c. Suppose the answer to part b is b1=4 (it is not, but to avoid compounding any mistakes, assume it is to answer the following). What is the value of b0?
d. Continue to assume that b1=4. What is the 90% confidence interval for the true population slope coefficient β1?