5. In an article in IEEE Transactions on Instrumentation and Measurement (2001.

Question

5. In an article in IEEE Transactions on Instrumentation and Measurement (2001. Vol. 50, pp. 2033-2040) powered mixtures of coal and limestone were analyzed for permeability. The errors in the density measurement were the response (under the "Density" column) Dielectric Constant 2.05 2.15 2.25 Loss Factor 0.016 0.02 0.022 0.023 0.026 0.028 0.031 0.34 0.039 0.042 0.045 ensi 0.749 0.798 0.849 0.877 0.929 0.963 0.997 1.046 1.133 1.17 1.215 2.47 2.54 2.64 2.85 2.94 3.05 (a) Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent variables and the dependent variables (b) Compute the residuals (c) Compute SSE and estimate the variance (d) Compute the coefficient of determination, R2, and adjusted coefficient of multiple determination, R2Adjusted Comment on their values (e) Find the standard error of the individual coefficients (f) Use a t-test to test for significance of the individual coefficients at ?-0.05. Comment on your results

Explanation / Answer

a) density^ = -0.110498593 + 0.40717 * dielectric + 2.1079636*loss_factor

b) see the table below

c) SSE =

variance = SSE/df_residual = 0.00007804342638

d) R^2 =

R^2_adj =

e)

f) if p-value < 0.05 ,the variable is significant

here dielctric constant is significant ,but loss factor is not

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SUMMARY OUTPUT Regression Statistics Multiple R 0.998677806 R Square 0.997357359 Adjusted R Square 0.996696699 Standard Error 0.008834219 Observations 11 ANOVA df SS MS F Significance F Regression 2 0.235634562 0.117817281 1509.637471 4.877E-11 Residual 8 0.000624347 7.80434E-05 Total 10 0.236258909 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.110498593 0.250067554 -0.441874971 0.670280599 -0.687155407 0.466158221 dielectric constant 0.407173897 0.168170109 2.421202547 0.041771643 0.01937293 0.794974865 loss factor 2.10796936 5.833619682 0.361348438 0.727196109 -11.34438175 15.56032047

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