Question

In: Statistics and Probability

Y (tensile strength given in Mpa) X (material type) 5.109 Butyl Rubber 7.896 Butyl Rubber 8.101...

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

Consider a dataset providing the tensile strength of a various types of polymers

(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?

Solutions

Expert Solution

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


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