and if there necessary calculation show the steps clearly Problem 3 Powdered mix

Question

and if there necessary calculation show the steps clearly Problem 3 Powdered mixtures of coal and limestone were analyzed for permittivity. The errors in the density measurement were the response. The following results are obtained. Densi 0.749 0.798 0.849 0.877 0.929 0.963 0.997 1.046 1.133 1.17 1.215 Dielectric Constant 2.05 2.15 2.25 2.3 Loss Factor 0.016 0.02 0.022 0.023 0.026 0.028 0.031 0.034 0.039 0.042 0.045 2.47 2.54 2.64 2.85 2.94 3.05 Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent variables and the dependent variable a. b. Compute the residuals. c. Compute SSE and estimate the variance d. Compute the coefficient of determination, R, and adjusted coefficient of multiple determination, R adjusted. Comment on their values. Construct the ANOVA table and test for significance of regression. your results. Find the standard error of the individual coefficients. Use a t-test to test for significance of the individual coefficients at = 0.05 Comment on your results. Construct 95% CIs on the individual coefficients. Compare your results with those found in part (g) and comment e. Comment on f. g. h.

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 =

f)

g) 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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