Question

Moissanite is a popular abrasive material because of its extreme hardness. Another important property of moissanite is elasticity. The elastic properties of the material were investigated in the Journal of Applied Physics (Sept. 1993). A diamond anvil cell was used to compress a mixture of moissanite, sodium chloride, and gold in a ratio of 33:99:1 by volume. The compressed volume, y, of the mixture (relative to the zero-pressure volume) was measured at each of 11 different pressures (GPa). The results of the simple linear regression are displayed here. a. What is the estimated model? Interpret intercept, Bo and slope, B1. b. What is the value of the coefficient of determination? Interpret this. c. Test the hypothesis that pressure contributes no information for the prediction of the volume when a linear model is used. Draw the appropriate conclusions. (use a=0.05) d. Check the residual plot and comment if a linear model is appropriate.

Answer 1

a) is zero Estimated model is } = Bot B x Y = 98.615 + (-0,25559)x Interpretation B When value of x then predicted y equals intercept or po B, = When value of x is changed by 1 unit then change in û is (-0.25559) or slope value. b) coefficient of determination = 98.98 % Interpretation 98.98) varication in y the model. c) 8 Hoiß,=0 vs Hiiß, to t= ß,ß. -0.2555g-o - 29.54798 0.00865 2 is explained by Se LB) to oas, 9 a/2=0.025 taso x=0.05 n-2= to .025,9 = 2.2622 t sta Hoi d) The plot Fail to reject Model is not significant. is such that residual contained inside a curved plot, then it indicateds non-linearity. This eo also mean the some other predictors are required in the model.