Analysis of Regression Models and Residual Diagnostics in Various Real-World Applications

Study on regression models and diagnostic techniques in statistics.

Chloe Martinez

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Analysis of Regression Models and Residual Diagnostics in Various Real-WorldApplications8.4Elasticity of moissanite.Moissanite ispopular abrasive material because of its extremehardness.Another important property of moissanite iselasticity.The elastic propertiesof the material were investigated in the Journal of Applied Physics (September 1993). Adiamond anvil cell was used to compress a mixture of moissanite, sodium chloride, andgold in a ratio of 33.99:1 by volume. The compressed volume, y, of the mixture (relativeto the zero-pressure volume) was measured at each of 11 different pressures (GPa). Theresults are displayed in the table (p.397).A MINITAB printout for the straight-lineregression model𝐸(𝑦)=𝛽0+𝛽1𝑥and a MINITAB residual plot are displayed at left.MOISSANITECOMPRESSED VOLUME y, %PRESSURE x, GPa1000969.493.815.890.230.487.741.686.246.985.251.683.360.182.962.682.962.681.768.4a.Calculate the regressionresiduals.The regression residuals are calculated and given below.RESI11.38508-0.21233-0.77653-0.64485-0.28219-0.42754-0.226250.046300.28529

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