1. Find the parameters of the linear regression equation using the method of least squares (OLS).
2. Find the equation of linear regression, using the matrix method.
3. Calculate the correlation coefficient and evaluate the resulting regression equation.
4. Calculate the coefficient of determination and assess the quality of a selected regression equation, these.
5. Calculate the average approximation error.
6. Evaluate the statistical significance of linear regression using the F-test Fisher.
7. Assess the statistical significance of the parameters of the linear regression equation (a and b), and correlation coefficient using the Student t-test.
8. Construct confidence intervals for the parameters of the linear regression equation (a and b) where the significance level α = 0,05.
 

There are data on the ten factories one industry on the levels of power per work X (ths. KWh / h) and the level of productivity per worker per year Y (thous. Pcs. Ed.):

X 9,4 6,0 6,1 7,2 6,8 9,4 10,5 11,4 11.5 12,1
Y 2 7 4 5 6 5 7 8 9 8