do not do B

6. Simple Linear Regression The effect of a certain additive on the drying time of paint has been measured and recorded as follows. x, additive conc. 4 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 y, drying time, 8.7 8.8 8.3 8.7 8.1 8.0 8.1 7.7 7.5 7.2 (a) Compute means and variances including the covariance of X and Y and then the correlation coefficient r. Do this part without MINITAB--you may use MINITAB to check your answers. Does the value of r justify looking for a linear relation between X and Y? (b) Using MINITAB, construct a scatter plot of drying time against additive concentration. (c) Carry out simple linear regression to obtain the least squares line for predicting drying time from additive concentration. Write it in the form involving only the estimated slope. = B(x ). Verify that B=r sy/sx (d) Compute the fitted value and residual e for each point; then plot the residuals vs fitted values. Comment on any pattern or lack of pattern in this plot. (e) Compute the sum of residuals squared and thus confirm that the coefficient of determination or R-sq is the ratio of (total error squared-sum of squared residuals) / total error squared. =