The data for this homework is drawn from a classic analysis which I'll describe in more detail later. The data come from an experiment in worsted yarn, where pieces of yarn were subjected to repeated loads (pulling) and the response was the number of cycles until failure (the yarn broke). The initial variables were: a1: length of the test specimen in mm a2: amplitude of the load cycle in mm a3: the load in g. These variables were coded by subtracting off a mean value and dividing by one-half the range of the data (units cancel), so that in this case x1 = (a1 - 300)/50, x2 = (a2 - 9), x3 = (a3 - 45)/5. As can be seen from the layout below, this was a designed experiment - the levels of the x_i's were chosen specifically to investigate the relationship between the x_i's and the response. The design used is known as a 3^3 factorial design - three factors were measured at all combinations of three levels each, low, medium and high. This deisgn allows for the estimation of both first and second order models. Some parts of the homework: Fit the first and second order models (including interactions) to the data. Test for the significance of the higher order effects as a group (partial F test). Plot the studentized residuals versus the fitted response. Comment. Examine the possibility of transforming the data. Produce a plot of the scaled Residual Sums of Squares using the Box-Cox transforms for both first and second order models, superimposed on a single plot (like the one I handed out in class). Using the transformation that you deem most appropriate, refit the least squares models and check for significance. Comment. Produce an ANOVA table for the final model you choose, and plot the sorted studentized residuals against normal quantiles. x1 x2 x3 y -1 -1 -1 674 0 -1 -1 1414 1 -1 -1 3636 -1 0 -1 338 0 0 -1 1022 1 0 -1 1568 -1 1 -1 170 0 1 -1 442 1 1 -1 1140 -1 -1 0 370 0 -1 0 1198 1 -1 0 3184 -1 0 0 266 0 0 0 620 1 0 0 1070 -1 1 0 118 0 1 0 332 1 1 0 884 -1 -1 1 292 0 -1 1 634 1 -1 1 2000 -1 0 1 210 0 0 1 438 1 0 1 566 -1 1 1 90 0 1 1 220 1 1 1 360