The following table gives the data for per capita income in thousands of US dollars with the percentage of the labor force in Agriculture, the average years of schooling of the population over 25 years of age, and overall health index for 15 developed countries in 2015 (data modified for educational purpose). Develop a multiple regression model for per capita income (dependent variable) using Excel and answer the questions below the table. You can use symbols Y, X1, X2 and X3 for the variables in your calculation. Show your computer output.

Country number	per capita	% of labor in Agriculture	Average yrs of schooling	Overall Health Index
1	32	12	7	70
2	42	10	12	80
3	41	8	11	77
4	38	9	9	75
5	40	10	10	76
5	52	5	16	95
7	44	7	10	82
8	41	7	11	80
9	46	6	13	85
10	50	8	15	92
11	47	7	11	90
12	53	4	16	98
13	48	6	14	90
14	47	7	12	85
15	50	6	15	90

Find the Y-intercept and slopes for the three independent variables and interpret them. Predict the per capita income when percentage of labor force in Agriculture is only 4, average years of schooling is 15. And Health Index is 100. 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. What are the degrees of freedom for Regression, Error and Total? Perform t-test for the statistical significance of individual coefficients. Plot the errors or residuals by countries and comment on the visible pattern. Plot the errors separately by each explanatory variable and comment on the visible patterns with respect to heteroscedasticity.