Applied Statistics and Probability for Engineers

(a) Calculate the least squares estimates of the slope and inter- cept. What is the estimate of ^2? Graph the regression model. ...

382 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION (a) Fit a simple linear model relating highway miles per gal- lon (y) to ...

shear strength and age were perfectly deterministic (no er- ror). Does this plot indicate that age is a reasonable choice of reg ...

384 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION Now consider the variance of. Since we have assumed that V(i)^2 , it ...

11-5 HYPOTHESIS TESTS IN SIMPLE LINEAR REGRESSION 385 where we have assumed a two-sided alternative. Since the errors iare NID( ...

386 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION although there is a linear effect of x, better results could be obtained ...

11-5.2 Analysis of Variance Approach to Test Significance of Regression A method called the analysis of variancecan be used to t ...

388 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION EXAMPLE 11-3 We will use the analysis of variance approach to test for s ...

11-6 CONFIDENCE INTERVALS 389 of the claim that if you can decrease the opponent’s rushing yardage by 100 yards the team will wi ...

390 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION EXAMPLE 11-4 We will find a 95% confidence interval on the slope of the ...

11-6 CONFIDENCE INTERVALS 391 Now is an unbiased point estimator of Yx 0 , since and are unbiased estimators of  0 and  1. T ...

392 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION or Therefore, the 95% confidence interval on is Minitab will also perfor ...

11-7 PREDICTION OF NEW OBSERVATIONS 393 Let Y 0 be the future observation at xx 0 , and let given by Equation 11-32 be the es- ...

394 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION which simplifies to Minitab will also calculate prediction intervals. Re ...

11-8 ADEQUACY OF THE REGRESSION MODEL 395 (d) Find a 95% prediction interval on steam usage when tem- perature is. Explain why t ...

396 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION is preferred. It requires judgment to assess the abnormality of such plo ...

11-8 ADEQUACY OF THE REGRESSION MODEL 397 the number of decimal places typical of computer output. A normal probability plot of ...

398 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION the analysis of variance identity in Equations 11-24 and 11-25, 0R^2 1 ...

11-8 ADEQUACY OF THE REGRESSION MODEL 399 (b) Prepare a normal probability plot of the residuals and interpret this graph. (c) P ...

400 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION 11-9 TRANSFORMATIONS TO A STRAIGHT LINE We occasionally find that the st ...