Question 1: Study the relationship between soil pH (x) and A1 (y). Data below.

1. Find the best polynomial model for this data.
2. Find the best model that involves a transformation of X and/or Y.
3. Which of these models in parts a) and b) is better?
4. Find a 94% Confidence interval for each of the  _j ’s in your models, and interpret.
5. Find a 93% Prediction Interval for y, when x = 4.25 using the model in part b). Does the point estimate for y when x = 4.25 using model a) fall in this interval?

"X" "Y"

4.01 1.2

4.07 .78

4.08 .83

4.1 .98

4.18 .65

4.2 .76

4.23 .4

4.27 .45

4.3 .39

4.41 .3

4.45 .2

4.5 .24

4.58 .1

4.68 .13

4.7 .07

4.77 .04

Question 2: The pull strength of a wire bond is an important characteristic. Pull strength (y), die height (x ₁ ), post height (x ₂ ), loop height (x ₃ ), wire length (x ₄ ), bond width on the die (x ₅ ), and bond width on the post (x ₆ ).

1. Analyze this data to find which linear model is the best fit for this data (give details on how you decided which model is best.
2. Report the amount of variation explained by the model you chose in part a).
3. Report your estimate of  ^
4. Find a 97% Confidence interval for each of the  _j ’s in your model, and interpret.
5. Holding all else fixed, how does a unit change in x ₄ change the average value of y?
6. For a specimen with x ₁ = 5.5, x ₂ = 19.3, x ₃ = 30.2, x ₄ = 90, x ₅ = 2, and x ₆ =1.85 find the predicted value of y (hint: you may not need all of these values since you may not include all of these variables in you model).

pullStrength – dieHeight – postHeight – loopHeight – wireLength – bondDie - bondPost

8.0 5.2 19.6 29.6 94.9 2.1 2.3

8.3 5.2 19.8 32.4 89.7 2.1 1.8

8.5 5.8 19.6 31.0 96.2 2.0 2.0

8.8 6.4 19.4 32.4 95.6 2.2 2.1

9.0 5.8 18.6 28.6 86.5 2.0 1.8

9.3 5.2 18.8 30.6 84.5 2.1 2.1

9.3 5.6 20.4 32.4 88.8 2.2 1.9

9.5 6.0 19.0 32.6 85.7 2.1 1.9

9.8 5.2 20.8 32.2 93.6 2.3 2.1

10.0 5.8 19.9 31.8 86.0 2.1 1.8

10.3 6.4 18.0 32.6 87.1 2.0 1.6

10.5 6.0 20.6 33.4 93.1 2.1 2.1

10.8 6.2 20.2 31.8 83.4 2.2 2.1

11.0 6.2 20.2 32.4 94.5 2.1 1.9

11.3 6.2 19.2 31.4 83.4 1.9 1.8

11.5 5.6 17.0 33.2 85.2 2.1 2.1

11.8 6.0 19.8 35.4 84.1 2.0 1.8

12.3 5.8 18.8 34.0 86.9 2.1 1.8

12.5 5.6 18.6 34.2 83.0 1.9 2.0

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Solution: The downloadable solution consists of 10 pages, 805 words and 8 charts.
Deliverable: Word Document