Establishing the properties of materials is an important problem in identifying a suitable substitute for biodegradable materials in the fast-food packaging industry. Consider the following data on product density (g/cm3) and thermal conductivity K-factor (W/mK) published in Materials Research and Innovation (1999, pp. 2–8).

(a) Estimate the intercept 0 and slope 1 regression coefficients.
Write the estimated regression line.

(b) Compute the residuals.

(c) Compute SSE and estimate the variance.

(d) Find the standard error of the slope and intercept coefficients.

(e) Show that SST SSR SSE.
(f ) Compute the coefficient of determination, R2. Comment on the value.
(g) Use a t-test to test for significance of the intercept and slope coefficients at 0.05. Give the P-values of each and comment on your results.
(h) Construct the ANOVA table and test for significance of regression using the P-value. Comment on your results and their relationship to your results in part (g).
(i) Construct 95% CIs on the intercept and slope. Comment on the relationship of these CIs and your findings in parts (g) and (h).
(j) Perform model adequacy checks. Do you believe the model provides an adequate fit?
(k) Compute the sample correlation coefficient and test for its significance at 0.05. Give the P-value and comment on your results and their relationship to your results in parts (g) and (h).

Transcribed Image Text:

Thermal Conductivity y Product Density x 0.0480 0.1750 0.0525 0.2200 0.0540 0.2250 0.0535 0.2260 0.0570 0.2500 0.0610 0.2765