In addition to a linear regression of true density on moisture content, the article cited in Exercise 6 considered a quadratic regression of bulk density versus moisture content.

Data from a graph in the article follows, along with a MINITAB output from the quadratic fit.

The regression equation is bulkdens
403 16.2 moiscont  0.706 contsqd 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 S
10.15 R-Sq
93.8% R-Sq(adj)
89.6%

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

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Analysis of Variance 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. Does the quadratic model appear to be useful? Carry out a test at significance level .05.

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.