The article “Physical Properties of Cumin Seed” (J. of Agric.

Engr. Res., 1996: 93–98) considered a quadratic regression of density on y 5 bulk x 5 moisture content. Data from a graph in the article follows, along with Minitab output from the quadratic fit The regression equation is Predictor Coef StDev T P Constant 403.24 36.45 11.06 0.002 moiscont 16.164 5.451 2.97 0.059 contsqd 0.7063 0.1852 3.81 0.032 Analysis of Variance Source DF SS MS F P Regression 2 4637.7 2318.9 22.51 0.016 Residual Error 3 309.1 103.0 Total 5 4946.8 StDev St Obs moiscont bulkdens Fit Fit Residual Resid 1 7.0 479.00 481.78 9.35 2.78 0.70 2 10.3 503.00 494.79 5.78 8.21 0.98 3 13.7 487.00 492.12 6.49 5.12 0.66 4 16.6 470.00 476.93 6.10 6.93 0.85 5 19.8 458.00 446.39 5.69 11.61 1.38 6 22.0 412.00 416.99 8.75 4.99 0.97 StDev Fit Fit 95.0% CI 95.0% PI 491.10 6.52 (470.36, 511.83) (452.71, 529.48)

a. Does a scatter plot of the data appear consistent with the quadratic regression model?

b. What proportion of observed variation in density can be attributed to the model relationship?

c. Calculate a 95% CI for true average density when moisture content is 13.7.

d. The last line of output is from a request for estimation and prediction information when moisture content is 14.

Calculate a 99% PI for density when moisture content is 14.

e. Does the quadratic predictor appear to provide useful information? Test the appropriate hypotheses at significance level .05.