An engineer performed an experiment to determine the effect of $\mathrm{CO}_{2}$ pressure, $\mathrm{CO}_{2}$ temperature, peanut moisture, $\mathrm{CO}_{2}$ flow rate, and peanut particle size on the total yield of oil per batch of peanuts. Table B. 7 summarizes the experimental results.

a. Fit a multiple linear regression model relating yield to these regressors.

b. Test for significance of regression. What conclusions can you draw?

c. Use $t$ tests to assess the contribution of each regressor to the model. Discuss your findings

d. Calculate $R^{2}$ and $R_{\text {Adj }}^{2}$ for this model. Compare these values to the $R^{2}$ and $R_{\text {Adj }}^{2}$ for the multiple linear regression model relating yield to temperature and particle size. Discuss your results.e. Find a $95 % \mathrm{CI}$ for the regression coefficient for temperature for both models in part d. Discuss any differences.

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Pressure Temp. Moisture (bars) (C) (% by weight) Flow Rate (L/min) Particle Size (mm) Yield 415 25 5 40 1.28 63 550 25 5 40 4.05 21 415 95 5 40 4.05 36 550 95 5 40 1.28 99 415 25 15 40 4.05 24 550 25 15 40 1.28 66 415 95 15 40 1.28 71 550 95 15 40 4.05 54 415 25 5 60 4.05 23 550 25 5 60 1.28 415 95 550 95 415 25 15 550 25 15 415 95 15 550 95 15 555555 5 60 1.28 80 60 4.05 33 8888 60 1.28 63 4.05 21 4.05 44 1.28 96