ACME company is interesting in making golf balls with maximum traveling distance

Question

ACME company is interesting in making golf balls with maximum traveling distance. They considered three important factors with different levels.

Dimple depth (low, high)

Number of dimples (250,500)

Shape of dimple (circular, elliptical)

Identify the main factors that maximize the travelling distance of the golf ball using full factorial design.

Standard Order (SO)

Experiment Order (EO)

Factor

Distance (m)

1

2

Low

250

Circular

200,250, 225

2

1

Hi

250

Circular

275, 250, 225

3

3

Low

500

Circular

225, 300, 210

4

7

Hi

500

Circular

250, 300, 350

5

6

Low

250

Elliptical

175,225, 200

6

5

Hi

250

Elliptical

320, 330, 350

7

8

Low

500

Elliptical

250, 300, 175

8

4

Hi

500

Elliptical

300, 325, 350

Standard Order (SO)

Experiment Order (EO)

Factor

Distance (m)

1

2

Low

250

Circular

200,250, 225

2

1

Hi

250

Circular

275, 250, 225

3

3

Low

500

Circular

225, 300, 210

4

7

Hi

500

Circular

250, 300, 350

5

6

Low

250

Elliptical

175,225, 200

6

5

Hi

250

Elliptical

320, 330, 350

7

8

Low

500

Elliptical

250, 300, 175

8

4

Hi

500

Elliptical

300, 325, 350

Explanation / Answer

we have ANOVA table here

‘**’

here only d=dimple depth has p-value < 0.05 so that effect has only ignificant in the regression.

hence except dimple depth there is no effect in the regression.

R-code for the problem is

y=c(
200,
250,
225,
275,
250,
225,
225,
300,
210,
250,
300,
250,
175,
225,
200,
320,
330,
350
)
d=as.factor(rep(rep(seq(1,2),each=3),3))
n=as.factor(c(rep(1,6),rep(2,9),rep(1,3)))
s=as.factor(c(rep(1,12),rep(2,6)))

fit=lm(y~d+n+s)
anova(fit)

Analysis of Variance Table Response: y Df Sum sq mean sq F value Pr(>F) d 1 16200.0 16200.0 9.9066 0.007127 n 1 756.2 756.2 0.4625 0.507566 s 1 1600.0 1600.0 0.9784 0.339375 Residuals 14 22893.8 1635.3 --- Signif. codes: 0 ‘***’ 0.001

‘**’

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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