For the data

x1	x2	y
1	2	3.1
2	4	5.9
3	5	8.1
4	3	7.3

(i) Derive using the OLS the estimators of the parameters of the linear regression model y = ₀+ ₁x₁+ ₂x₂.

Show the complete derivation process.

Calculate manually the estimators of the parameters (on paper, using a calculator, no Excel). (ii) Calculate manually the coefficient of determination and the adjusted coefficient of determination. Write a sentence what the coefficient of determination represents. (iii) Use Excel to test whether the two independent variables are jointly statistically related to variable y. Run the test at significance level 0.01. Think: If you decide that the two independent variables are jointly statistically unrelated to variable y, is there a need to run a test whether each independent variable is significant? (iv) Depending on the result of your hypothesis testing in (iii), test whether each independent variable is significant in the model.