In a certain industrial process, an automatic grinding machine that produces the least surface roughness is to be selected. Four repeat tests were run, using machines submitted by three different suppliers and the following data were obtained. Determine with 90% confidence whether there is any significant difference between machines, and if so, which one should be selected:
Grinding machines
Surface Roughness: 20 18 19 21 11 12 14 13 15 14 16 15
Regression: Use a scatterplot to explain the relationship between X and Y. What do you expect for the sign of B1 and magnitude of r^2? After running the regression model in Minitab, what is the estimated regression equation? Interpret the estimate of BO in the words of the problem. Do the same for B1. BO = 1.49. Conduct a test that the true slope of the model differs from 0. Explain how to use the output of the regression for the test. Relate the conclusion of your test to the scatterplot that you generated in (1). Use the generated plots of the regression model (histogram of the residuals) to check the normality assumption of your model. While there is no need for a statistical test, you must compare the shape to a normal distribution pdf. Generate the fitted line plot for this regression. Generate a prediction interval for y* and a confidence interval for (y) when x* = X (average of given X's). Note that x* is a point in units that we are interested in predicting the minutes for it. Here, as an example, we use X = 6 (average of column 'unit') as x*. So, in general, you can pick any value for x. To generate the intervals, we need to run the regression model again.