The following data is a subset of data obtained in an experiment to study the re

Question

The following data is a subset of data obtained in an experiment to study the relationship between x = soil pH and y = A1. Concentration/EC:

A cubic model was proposed in an article, but the version of Minitab used by the author of the present text refused to include the x3 term in the model, stating that "x3 is highly correlated with other predictor variables." To remedy this, x = 4.3563 was subtracted from each x value to yield x' = x x. A cubic regression was then requested to fit the model having regression function

y = 0* + 1*x' + 2*(x')2 + 3*(x')3

The following computer output resulted:

0.3725    

1.4034    

1.6918    

0.5957    

(a) What is the estimated regression function for the "centered" model? (Round your answers to four decimal places.)

(b) What is the estimated value of the coefficient 3 in the "uncentered" model with regression function y = 0 + 1x + 2x2 + 3x3? (Round your answer to four decimal places.)

What is the estimate of 2? (Round your answer to four decimal places.)

(c) Using the cubic model, what value of y would you predict when soil pH is 4.5? (Round your answer to four decimal places.)

(d) Carry out a test to decide whether the cubic term should be retained in the model. (Use = 0.05.)
State the appropriate null and alternative hypotheses.

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

State the conclusion in the problem context.

x   3.97 4.07 4.09 4.12 4.22 4.22 4.24 4.27 4.32 4.42 4.44 4.55 4.63 4.66 4.67 4.81 y   1.22 0.79 0.83 0.98 0.66 0.77 0.40 0.46 0.38 0.31 0.19 0.23 0.11 0.11 0.05 0.02

Explanation / Answer

answer:

Using Minitab

Cubic regreession model:

Polynomial Regression Analysis: y versus x

The regression equation is
y = 84.6 - 49.9 x + 9.90 x^2 - 0.662 x^3

S = 0.102429 R-Sq = 93.8% R-Sq(adj) = 92.1%

Analysis of Variance

Source DF SS MS F P
Regression 3 1.74032 0.580108 55.29 0.000
Error 11 0.11541 0.010492
Total 14 1.85573

Sequential Analysis of Variance

Source DF SS F P
Linear 1 1.67455 120.15 0.000
Quadratic 1 0.06455 6.64 0.024
Cubic 1 0.00122 0.12 0.739

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.