Problem3: The reliability level Y of a fuel tank depends on the age in years of

Question

Problem3: The reliability level Y of a fuel tank depends on the age in years of the automatic line leak detectors to prevent overfilling and sacrificial anodes on steel tanks to prevent corrosion XI and the Brominated flame retardants variety X2 to control fire. The values of X1 and X2 and the corresponding reliability levels in six fuel tanks are given in the following table X2 20.0 19.2 22.3 18.9 85 92 50 65 57 60 70 80 Inter the table data in Minitab correctly, then carry out the analysis. 87 90 96 20.4 a) Find the correlation of x1, x2 and interpret. b) Find the regression equation and interpret the coefficients? c) Test the model validity (significance) of the model? d) Which independent variable is linearly related to Y? and why? e) What percentage of variation in the reliability level is explained by the above regression model? Estimate the level of reliability and find 95% confidence interval and 95% prevention interval for the estimated reliability level if the age of the automatic line leak detector is 5.8 and the variety of the Brominated flame retardant is 19.7

Explanation / Answer

a)

Correlation between the two is -0.1393

b)

y=59.59+0.36*X1+0.37*X2

c)

F>Sign F and hence the model is significant (atleast one of the independent variables affect the dependent variables)

d)

X1 is linearly related to Y and one can say that based on the p-value (is less than 0.05)

e)

r^2 is 0.8867 which means 88.67% of the variation in reliability level is explained for by the regression model

To run in minitab, please follow the procedure below: -

a) Go to STAT

b) Go to Regression and again Regression

c) Enter Response and Predictor Variables

d) Here, response would be the reliability level of a fuel tank and predictor would be age in years of the automatic line leak detectors to prevent overfilling and sacrificial anodes on steel tanks to prevent corrosion and Brominated flame retardants variety to control fire

SUMMARY OUTPUT Regression Statistics Multiple R 0.94 R Square 0.89 Adjusted R Square 0.81 Standard Error 1.71 Observations 6 ANOVA df SS MS F Significance F Regression 2 68.57 34.28 11.74 0.04 Residual 3 8.76 2.92 Total 5 77.33 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 59.59 14.06 4.24 0.02 14.85 104.33 X1 0.36 0.07 4.84 0.02 0.12 0.59 X2 0.37 0.63 0.59 0.60 -1.63 2.37

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