Data from Exercise 1.9 relating plant biomass Y to total accumulated solar radiation X was used to fit a no-intercept model.  and e were determined from the regression equation. The matrix W (8 × 4)...

Data from Exercise 1.9 relating plant biomass Y to total accumulated solar radiation X was used to fit a no-intercept model.
 and e were determined from the regression equation. The matrix W (8 × 4) was defined as and the following matrix of sums of squares and products was computed.

(a) Determine the length of each (column) vector in W.

(b) Compute the angles between all pairs of vectors.

(c) Use the lengths of the vectors and the angles between the vectors to show graphically the regression results. What is the dimension of the X-space? Why is the angle between X and
 zero? Estimate the regression coefficient from the figure you construct.

Exercise 1.9

A linear regression was run on a set of data using an intercept and one independent variable. You are given only the following information:

(2) The t-test for H₀: β₁
= 0 was non significant at the α = .05 level. A computed t of −4.087 was compared to t(.05,2) from Appendix Table A.1.

(3) The estimate of σ²
was s²
= 1.75.

(a) Complete the analysis of variance table using the given results.

(b) Compute and interpret the coefficient of determination R².