In: Statistics and Probability
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?
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