The following table gives the data for per capita income in thousands of US dollars with the percentage of the labor force in Agriculture and the average years of schooling of the population over 25 years of age for 15 developed countries in 2000 (data modified for educational purpose). Develop a multiple regression model for per capita income (dependent variable) using Excel or MegaStat and answer the questions below the table. You can use symbols Y, X1 and X2 for the variables in your calculation. Show your computer output.
Country number per capita % of labor in Agriculture Average years of schooling
1 20 9 7
2 26 10 12
3 24 8 11
4 21 7 11
5 22 10 12
5 42 4 16
7 27 5 11
8 24 5 9
9 28 6 12
10 32 8 14
11 30 7 12
12 40 4 16
13 34 9 14
14 30 5 10
15 35 8 13
Find the Y-intercept and slopes for the two independent variables and interpret them. Predict the per capita income when percentage of labor force in Agriculture is only 3 and average years of schooling is 15. Find the overall explanatory power (Coefficient of Determination) of the model and interpret it. Also find the adjusted coefficient of Determination and interpret it. Find the standard error of estimate. From the ANOVA table find SSR, SSE and SST and the F-value. Perform the F-test and comment on the overall usefulness of the model Perform t-test for the statistical significance of individual coefficients.