Question

Exercise 6.3 Let us consider the salary (y), the years of experience(K1) and the years of schooling (X2) for 50 employees of the Georgia Pacific Company in Crossett, Arkansas. Our goal is to build a model that will satisfy all of our assumptions, so that we can use years of experience and years of schooling to predict salaries. The data is presented below 12 14 12 12 16 99139 52624 50594 53272 65343 46216 54288 16105 12 65726 41983 62309 14 17 14 19 12 47780 12 15 15 53610 33697 22444 32562 66537 67447 64785 61581 0678 51301 39346 14 25 16 16 13 12 32586 71235 36530 2745 67282 80931 32303 38371 12 16 16 12 14 14 10 12 58667 18 16 20521 26 65929 41721 82641 12 49727 16 16 16 STEP 1: Start with the simplest of regression models:Y-Po+BX+P2X2+&. Plot x versus y and then fit this model. What kind of pattern do you see? What does this pattern suggest? STEP 2: Calculate the residuals. Are 95% of the residuals within 2s of the mean? STEP 3: Plot the residuals versus y. Do you see any curvature or patterns? Are any of the assumptions violated? STEP 4: Now add an X-trm to the model and fit the model y-Ao +MX1 + β2X2 + β3Xi + ε Calculate the residuals. Are 95% of the residuals within 2s of the mean? STEP S: Plot these new residuals versus y. Do you see any trends or patterns? If so, what is being suggested? Is there anything we can do? STEP 6: Let us make a transformation by taking the natural logarithm of y and use a new model. ln'sA, +MX1 + X2 +A,Kf+ε Plot logy versus x, what do you see here and what does the plot suggest? STEP 7: Plot the residuals versus y. Now do you see any pattern? Can we now conclude that the assumption of constant variance is satisfied? STEP&: Now let us check for Normality. Construct a normal probability plot. What kind of shape do you see? Does normality appear to be violated? STEP 9: Can we now conclude that the model is a good and valid model to use in predicting salary based on years of experience?

Essay questions

1. in exercise 6.3 step 5, what can you say about the assumption of constant variance?

2. in exercise 6.3 step 7, what can you say about the assumption of constant variance?

3. in exercise 6.3 step 8, what can you say about the assumption of normality

Answer 1

of . Fit Reselsion moie -> ceick of tCn

Residual Plots for Y Residual Plots for Y Normal Probability Plot Versus Fits E SA 10 -10000 10000 1000 20000 Residual 20000 40 60000 000 Histogra 2000 E 100N 1000 1 5 10 15 20 25 30 3540 45 50 Reidual

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