Econometrics: Problem 0004

For 20 enterprises in the region, the dependence of the output per employee y (thousand rubles) on the commissioning of new fixed assets x1 (% of the value of the assets at the end of the year) and on the share of highly qualified workers in the total number of workers x2 (%) ...

room
enterprises x1 x2
1 7,0 4,1 11,0
2 7,0 3,7 13,0
3 7,0 3,9 15,0
4 7,0 4,0 17,0
5 7,0 4,3 18,0
6 7,0 4,8 19,0
7 8,0 5,3 19,0
8 8,0 5,4 20,0
9 8,0 5,1 20,0
10 10,0 6,8 21,0
11 9,0 6,0 21,0
12 11,0 6,4 22,0
13 9,0 6,9 22,0
14 11,0 7,2 25,0
15 12,0 8,0 28,0
16 12,0 8,2 29,0
17 12,0 8,1 30,0
18 12,0 8,6 31,0
19 14,0 9,6 32,0
20 14,0 9,0 36,0

Required:
1. Build a linear multiple regression model. Write a standardized multiple regression equation. On the basis of standardized regression coefficients and average elasticity coefficients, rank the factors according to the degree of their influence on the result.
2. Find the coefficients of pair, partial and multiple correlation. Analyze them.
3. Find the corrected multiple determination coefficient. Compare it with the unadjusted (overall) coefficient of determination.
4. Using F-Fisher's criterion to evaluate the statistical reliability of the regression equation and the coefficient of determination Ryx1x2.
5. Using the Student's t-test to assess the statistical significance of the parameters of pure regression.
6. With the help of Fisher's particular F-criteria, evaluate the feasibility of including the factor x1 after x2 and the factor x2 after x1 in the multiple regression equation.
7. Make a linear pairwise regression equation, leaving only one significant factor.
8. Check the calculations in MS Excel.