In an article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 2033–2040) powdered mixtures of coal and limestone were analyzed for permittivity.
The errors in the density measurement were the response.

(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 variable.

(b) Compute the residuals.

(c) Compute SSE and estimate the variance.

(d) Compute the coefficient of determination, R2, and adjusted coefficient of multiple determination, R2 Adjusted.
Comment on their values.

(e) Construct the ANOVA table and test for significance of regression.
Comment on your results.

(f) Find the standard error of the individual coefficients.
(g) Use a t-test to test for significance of the individual coefficients at 0.05. Comment on your results.
(h) Construct 95% CIs on the individual coefficients.
Compare your results with those found in part (g) and comment.
(i) Perform a model adequacy check, including computing studentized residuals and Cook’s distance measure for each of the observations. Comment on your results.
( j) Compute the variance inflation factors and comment on the presence of multicollinearity.

Transcribed Image Text:

Density 0.749 Dielectric Constant Loss Factor 2.05 0.016 0.798 2.15 0.02 0.849 2.25 0.022 0.877 2.3 0.023 0.929 2.4 0.026 0.963 2.47 0.028 0.997 2.54 0.031 1.046 2.64 0.034 1.133 2.85 0.039 1.17 2.94 0.042 1.215 3.05 0.045