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). 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. Regression Analysis: Volume versus Pressure Model Summary s R-sq R-sq(adj) R-sq (pred) 0.648350 98.989 98.879 97.899 Coefficients VIE Term Constant Pressure Coef SE Coef T-Value P-value 98.615 0.404 244.26 0.000 -0.25559 0.00865 -29.56 0.000 1.00 Using MINITAB, the residual plot is: Pressure

Answer 1

ORTE a ) de = independent variable = L = dependent variable pressure volume - 025559 y on œ from given model we have volume = (98.615) pressure then we know y = ßot ßiæ the regression equation of then by comparing we have pr= -0.25559 slope fo = y-intercept 98615 then Bo which is intercept ra represent the volume which is estimated at pressure at value of LEO 98.615 1) the average -0.25559 = slope interpret the decrease in the volume due to the pressure The relationship between volume and pressure for gisen data is negatively.conelated. 6) from a given information coefficient of delermination 98-984 the 98-984 of the ie, it interpret Variability in the volume is accounled It is fit model the given regression model. to predict the volume at given pressure ty CS Scanned with CamScanner

p c) Here we have to test Ho Biro ie there is no linear relation ship between volume and pressure Hii pito ie there is linear relationship between volume and pressure Under Ho, the test statistic is to - Bu 0.25559 0 0 0965 seca - 29.5480 0.00865 -0.25559 A Here x=0.05 then critical value t tilt oos tio.o.025 - 2.200 of tn 1212 2 we 50 Thus Itol > tio o.o25 reject Ho at level of significance and conclude that there is linear relationship between volume and pressure d) Given plot is such that the residuals are contain- ed inside a curved plot, then it indicate non- linearity. The assumed relationship between pressure and volume is non-linear. CS Scanned with CamScanner

t table as follows:

7:43 62.0 KB/S 774 Edit 26 Х t-distribution Confidence Level 85% 90% 95% 98% 60% 70% 80% 99% 99.8% 99.9% 2 Tailed 1 Tailed 0.40 0.20 0.30 0.15 0.20 0.10 Level of Significance 0.15 0.10 0.05 0.02 0.075 0.05 0.025 0.01 0.01 0.005 0.002 0.001 0.001 0.0005 26.30 12.39 8.499 6.835 5.946 5.403 5.039 0.039 4.780 2.822 3.250 df 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 18 19 20 21 22 23 24 25 4.586 4.437 1.376 1.963 3.133 4.195 6.320 12.69 31.81 63.67 1.060 1.385 1.883 2.278 2.912 4.271 4.271 6.816 9.520 0.978 1.250 1.637 1.924 2.352 3.179 4.525 5.797 0.941 1.190 1.533 1.778 2.132 2.776 3.744 4.596 0.919 1.156 1.476 1.699 2.015 2.570 3.365 4.030 0.906 1.134 1.440 1.650 1.943 2.447 3.143 3.707 0.896 1.119 1.415 1.617 1.895 2.365 2.999 3.500 0.889 1.108 0.00% 1.397 1.592 1.860 2.306 2.897 3.356 0.000 0.883 1.100 1.383 1.574 1.833 2.262 0.879 1.372 1.093 V. 1.559 1.813 2.228 2.764 3.170 0.875 0.00 1.088 1.363 1.305 1.548 1.796 2.201 2.719 3.106 0.873 1.083 1.356 1.538 1.782 2.179 2.682 3.055 0.870 1.079 1.350 1.530 1.771 2.160 2.651 3.013 0 000 0.868 1.076 1.345 1.523 1.761 . 15 2.145 2.625 2.977 0.866 1.074 1.341 1.517 1.753 2.131 2.603 2.947 0.865 1.071 1.337 1.512 1.746 2.120 2.584 2.921 0.863 1.069 1.333 1.508 1.740 2.110 2.567 2.899 0.862 1.067 1.330 1.504 1.734 2.101 2.553 2.879 0.861 1.000 1.066 1.328 1.500 1.000 1.729 2.095 2.093 2.540 2.861 0.860 1.064 1.325 1.497 19 1.725 .125 2.086 2.529 2.840 0.859 1.063 1.323 1.494 1.721 2.080 2.518 2.832 0.858 1.061 1.321 1.717 2.074 2.074 2.509 2.819 0.857 1.060 1.319 1.489 1.714 2.069 2.500 2.808 0.857 1.487 1.711 2.064 2.493 2.797 0.856 1.058 1.485 1.708 2.060 2.486 2.788 0.856 1.058 1.315 1492 1.483 1.706 2.056 2.479 2.779 0.855 1.057 1.314 ora 1.482 1.703 2.052 2.473 more 2.473 2.771 1994 0.855 1.056 1.313 1.480 1.701 2.048 2.468 2.764 MORALES 1120 1.055 Icon 0.854 1.311 1.479 1.699 2.045 2.463 2.757 LE 0.854 1.055 1.310 2019 20 1.477 1.697 Movie 2.042 2.458 2.750 0.851 1.050 1.303 Tied 10 201 202 203 1.468 1.684 2.021 2.424 2.705 dou 0 0 100 0.849 1.047 1.299 1.462 1.676 2.009 2.404 2.678 0.848 0 1 1.045 1.296 1.458 1.671 2.000 2.391 2.661 0.847 1.044 1.294 1.456 1.667 1.994 2.381 2.648 0.846 1.043 1.292 1.453 1.664 1.990 2.374 2.639 0.846 1.042 1.291 1.452 1.662 1.987 2.369 2.632 0.845 1.042 1.290 1.451 1.660 1.984 2.365 2.626 19.65 9.937 7.115 5.876 5.201 4.783 4.500 4.297 4.297 4.144 4.025 3.930 3.930 3.852 3.788 3.733 3.687 3.646 3.611 3.580 4.318 4.221 4.141 4.073 4.015 3.965 3.922 3.884 3.850 3.552 3.820 1.492 1.059 1.318 1.316 27 28 29 30 40 50 60 70 80 90 100 3.528 3.505 3.485 3.467 3.451 3.435 3.421 3.409 3.397 3.386 3.307 3.262 3.232 3.211 3.196 3.184 3.174 3.792 3.768 3.746 3.725 2707 3.707 con 3.690 3.674 3.660 3.646 3.551 3.496 3.460 10 3.435 3.417 3.402 3.391 0842 1.036 1.282 1.440 1.645 1.960 2.327 2.576 3.091 3.291 סס w DD Tools Mobile View Share PDF to DOC