Exercise B Let consider the model yi = Bi + B2.xi + By. Vrite; for ie {1,..., n}, The variables &; are gaussian, independent with expectation 0 and variance o?. 1. Write the matricial equation with t(3) = (31, 82, 83). 2. For a dataset, with n = 100, we find : ? 222 -569 t (X).X= ? 3767 ? t ( X ) . Y = -4505 t(Y).Y = 651900 ? 1408 544 1610 What are the values of ' 3. What is the mean of the x;? 4. Whatare the estimationsof 81, B2 and 83? 5. What is the estimationof o?? 6. Computea confidenceintervalfor 82 with level 95%. 7. Perform the test 82 = 0 with respect B2 / 0 with level 10%. 8. Compute the coefficient of determination. 9. Computea confidenceintervalfor yn+ 1 at level 95%, knowing In+1 = 49. 10. Computea confidenceintervalfor yn+ 1 at level 95%, knowing In+1 = 25. 11. Which one is the biggest one? Why