The article The Undrained Strength of Some Thawed Permafrost Soils\' contained t

Question

The article The Undrained Strength of Some Thawed Permafrost Soils' contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x_1 = depth (m) x_2 = water content (%) The predicted values and residuals were computed using the estimated regression equation where x_3 = x_1^2, x_4 = x_2^2, and x_5 = x_1 x_2 y = -151.36 - 16.22 x_1 + 13.48 x_2 + 94 x_3 + 253x_4 + 492 x_3 (a) Use the given information to compute SSResid, SSTo, and SSRegr. (Round your answer to four decimal places if needed.) SSTo = SSResid = SSRegr = (b) Calculate R^2 for this regression model. ( if needed.) R^2 = (c) Use the value of R^2 from Part (b) and a 0.05 level of significance to conduct the appropriate model utility test. (Round the answer to two decimal places.] F = The null hypothesis is rejected

Explanation / Answer

SST = 1618.209286

SSResid = 390.6385608

SSReg = 1227.570725

b) R^2 =

c)

F =

sifnificance F = 0.0222 < 0.05

hence the null is rejected

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SUMMARY OUTPUT Regression Statistics Multiple R 0.870975456 R Square 0.758598245 Adjusted R Square 0.607722149 Standard Error 6.98783372 Observations 14 ANOVA df SS MS F Significance F Regression 5 1227.570725 245.514145 5.027955141 0.022229589 Residual 8 390.6385608 48.8298201 Total 13 1618.209286 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -151.3555106 134.0691513 -1.128936143 0.291638128 -460.519528 157.8085 -460.52 157.8085 x1 -16.21614389 8.831467771 -1.836177667 0.103651059 -36.58154509 4.149257 -36.5815 4.149257 x2 13.47558459 8.186859728 1.646001646 0.138381071 -5.403347801 32.35452 -5.40335 32.35452 x3 0.093527773 0.070927304 1.318642721 0.223785427 -0.070030883 0.257086 -0.07003 0.257086 x4 -0.252820574 0.127059832 -1.989775759 0.081801395 -0.545821073 0.04018 -0.54582 0.04018 x5 0.492237993 0.228130994 2.157698898 0.063014921 -0.033833021 1.018309 -0.03383 1.018309

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