The relation between polishing time and product diameters as well as type of product (casserole, other) is one which is useful to the company for estimating the polishing time for new products which are designed or suggested for design and manufacture. A necessary regression assumption is that the errors in such estimates are constant over the range of product diameters. A check of this assumption by plotting residuals from the regression against diameters is shown in the image below. In this case the errors appear to increase with increasing diameter of product.
If errors are in fact proportional to the diameters of products, the residuals from the regression of the logarithms of time versus product diameters will be constant. The student should run this transformed regression against diameters and the dummy variable for casseroles and check the plot of these residuals against product diameters. It is also useful to examine the coefficients of the regression line, translating them into an equation for estimated Y as opposed to estimated logarithm of Y.