11.19 A rubber additive made from cashew nut shells. Car- danol, an agricultural

Question

11.19 A rubber additive made from cashew nut shells. Car- danol, an agricultural byproduct of cashew nut shells, is a cheap and abundantly available renewable resource. In In- 013), researchers investigated the use of cardanol as an additive for natural rubber. Cardanol was grafted onto pieces of natural rubber latex and the chemical properties examined. One property of interest is the grafting efficiency (meas- ured as a percentage) of the chemical process. The researchers manipulated several independent variables in dustrial & Engineering Chemistry Research (May2

Explanation / Answer

#a)

Hypothesis:

H0: Model is adequate.

Vs

H1:Model is inadequate.

MTB > Regress;

SUBC>   Response 'y';

SUBC>   Nodefault;

SUBC>   Continuous 'x1' - 'x4';

SUBC>   Terms x1 x2 x3 x4;

SUBC>   Constant;

SUBC>   Unstandardized;

SUBC>   Rtype 2;

SUBC> GFOURPACK;

SUBC>   Tmethod;

SUBC>   Tanova;

SUBC>   Tsummary;

SUBC>   Tcoefficients;

SUBC>   Tequation;

SUBC>   TDiagnostics 0.

Regression Equation

y = 97.3 - 5.72 x1 - 3.357 x2 + 0.433 x3 - 1.68 x4

Regression Analysis: y versus x1, x2, x3, x4

Analysis of Variance

Source      DF   Adj SS   Adj MS F-Value P-Value

Regression   4 2208.21   552.05     4.38    0.091

x1         1   196.54   196.54     1.56    0.280

x2         1 1690.42 1690.42    13.43    0.022

x3         1   253.11   253.11     2.01    0.229

x4         1    68.14    68.14     0.54    0.503

Error        4   503.61   125.90

Total        8 2711.82

Interpretation: here p-value is 0.091. Which is greater than level of significance 0.05. Hence we reject the null hypothesis.

#b)

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)

11.2206 81.43%     62.86%      30.08%

Interpretation: R-sq value is 81.43%. Which means 81.43% has variation in the data.

#c)

Interpretation: S value in the model summary is 11.2206.which shows average distance of data points from the fitted line is about 11.2206% in grafting efficiency.

#d)

One-Sample T: x1, x2, x3, x4

Variable N   Mean StDev SE Mean      90% CI

x1        9 2.000 0.866    0.289 (1.463, 2.537)

x2        9 10.00   4.33     1.44 ( 7.32, 12.68)

x3        9 50.00 12.99     4.33 (41.95, 58.05)

x4        9 8.000 1.732    0.577 (6.926, 9.074)

Interpretation: all regression coefficient does not lie in the confidence interval. So we reject the null hypothesis.

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