Question

Consider a dataset providing the tensile strength of a various types of polymers . Answer the following.

(a) How many levels of qualitative input variable are present?

(b) How many input variables (?? variables) would you use to represent the qualitative input variable?

(c) Rewrite the given dataset in terms ? and ?? variables. Please write here how the 1st, 5th, 10th and 15th data points are represented in terms ? and ?? variables.

(d) Build a regression model using Analysis ToolPak and write down the estimates of the regression parameters.

(e) What is the tensile strength model prediction of Neoprene? [3 points]

Y (tensile strength given in Mpa)	X (material type)
5.109	Butyl Rubber
7.896	Butyl Rubber
8.101	Butyl Rubber
9.838	Butyl Rubber
6.168	Butyl Rubber
9.078	Butyl Rubber
7.854	Neoprene
7.003	Neoprene
14.454	Neoprene
11.323	Neoprene
12.911	Neoprene
6.244	Neoprene
3.851	Silicone Elastomers
5.202	Silicone Elastomers
3.034	Silicone Elastomers
4.973	Silicone Elastomers
5.126	Silicone Elastomers
3.405	Silicone Elastomers

Answer 1

a) there are 3 levels

b)

we need 2 variable

c)

y	x_Butyl_Rubber	x_Neoprene
5.109	1	0
7.896	1	0
8.101	1	0
9.838	1	0
6.168	1	0
9.078	1	0
7.854	0	1
7.003	0	1
14.454	0	1
11.323	0	1
12.911	0	1
6.244	0	1
3.851	0	0
5.202	0	0
3.034	0	0
4.973	0	0
5.126	0	0
3.405	0	0

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.74752262
R Square	0.558790068
Adjusted R Square	0.499962077
Standard Error	2.280733084
Observations	18
ANOVA
	df	SS	MS	F	Significance F
Regression	2	98.81971144	49.40985572	9.498710706	0.00216192
Residual	15	78.026151	5.2017434
Total	17	176.8458624
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	4.265166667	0.931105383	4.580756106	0.000360485	2.280562522
x_Butyl_Rubber	3.433166667	1.31678186	2.607240251	0.019811317	0.62651257
x_Neoprene	5.699666667	1.31678186	4.328482067	0.000596644	2.89301257

y^= 4.2652 + 3.4332 x_Butyl_Rubber + 5.7 x_Neoprene

e)

for Neoprene

y^= 4.2652 + 5.7

= 9.9652