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 (in g/cm3 ) and thermal conductivity K-factor (W/mK) published in Materials Research and Innovation (1999, pp. 2-8).Thermal Conductivity (y) 0.0480 0.0525 0.0540 0.0535 0.0570 0.0610 Product Density (x) 0.1750 0.2200 0.2250 0.2260 0.2500 0.2765a) Estimate the intercept β0 and β1 regression coefficients. Write the estimated regression line. b) Compute the residuals. c) Compute the SSE and estimate the variance. d) Find the standard error of the slope and intercept coefficients. e) Show that SST=SSR+SSEf) Compute the coefficient of determination, R2 . Comment on the value. g) Use a t-test for significance of the intercept and slope coefficients at α=0.05. Give the Pvalues of each and comment on your results. i) Construct 95% CIs on the intercept and slope. Comment on the relationship of these CIs and your findings in part (g) and (h).