Use the Scala statistical geometric approach utility functions for your calculations, developed for your assignments: Given the raw data as follows where X is the predictor and Y is the dependent variable. X = Vector ( 3.0, 4.0, 5.0), Y = ( 6.0, 9.0, 15.0) As per usual, decompose the X and Y vectors into components within a constant vector space and components within the orthogonal complement of the constant space, the variation space. Let w0 be the Y intercept of the regression line, and let w1 be the slope of the regression line. Let x = X Xbar // where Xbar is the vector of mean values therefore x is the variation vector Let y = Y Ybar // where Ybar is the vector of mean values, therefore y is the variation vector. What is the raw regression vector equation? Calculate the following using your code a. wo, w1 ( actual values, e.g. w0 = -8) b. x, y, yhat, error = y yhat ( actual vector values e.g., x = (-1, 0, 1), y = (-4,-1, 5) . . .. c. SST, SSR, SSE, MSE, RMSE, correlation coefficient, angle between x and y. I would like you to put this all together on a diagram so that can you actually see each of these statistical parameters, So: d. Sketch a triangle diagram in the variation space, Diagram 1, showing all your calculated vectors ( with their actual components). Also label the angle between x, y ... In particular, note the connections beween: e. SST in terms of y vector, e.g. SST is dot(y,y) value = ? f. SSR in terms of yhat vector value = ? g. SSE in terms of error vector value? h. How is MSE related to dot(error, error) and what is its value? i. since cos theta is the correlation coefficient, what is its relation to y and yhat? j. Most statistical packages return r^2. The square of the correlation coefficient, what does this mean in terms of SSR and SST?