The article "The Undrained Strength of Some Thawed Permafrost Soils" contained the accompanying data on the following.y shear strength of sandy soil (kPa)x₂-depth (m)x₂ water content (%)The predicted values and residuals were computed using the estimated regression equation9-145.41-14.24x, +12.70x₂ +0.079x,-0.236 +0.441xwhere x₂-x₂²x₂-x₂², and x ₁2Y14.7*29.1 31.648.0 36.5 27.125.6 36.7 25.810.0 6.0 39.216.0 7.0 39.316.8 7.0 38.420.7 7.4 34.038.8 8.3 33.716.9 6.4 28.027.0 8.1 33.016.0 4.6 26.424.9 9.8 37.97.3 2.8 34.512.8 1.9 36.3Predicted y Residual23.8347.0726.4610.7714.5716.8823.3825.0716.2324.3115.0628.6415.088.15-9.130.93-0.86-0.771.43-0.08-2.6813.730.672.690.94-3.74-7.784.65(a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.)SSTO-1x|xSSResid-SSRegr -Ix(b) Calculate R² for this regression model. (Round your answer to three decimal places.)R²-XHow would you interpret this value?O The value R² gives the percentage of observed variation in water content that can be explained by the fitted model.O The value R² gives the percentage of observed variation in shear strength of sandy soil that can be explained by the fitted model.O The value R² gives the percentage of water content values in the sample that are equal to the values predicted by the model.The value R² gives the percentage of shear strength of sandy soil values in the sample that are equal to the values predicted by the model.(c) Use the value of R2 from part (b) and a 0.05 level of significance to carry out a model utility Ftest.Calculate the test statistic. (Round your answer to two decimal places.)F-XUse technology to calculate the value. (Round your answer to four decimal places.)P-value=1xWhat can you conclude?Fail to reject H. We have convincing evidence that the multiple regression model is useful.Reject H. We do not have convincing evidence that the multiple regression model is useful.Reject H. We have convincing evidence that the multiple regression model is useful.Fail to reject H. We do not have convincing evidence that the multiple regression model is useful

y^=-145.41-14.24x1+12.70x2+0.079x3-0.236x4+0.441x5where, x3=x12, x4=x22, and x5=x1x2

The article The Undrained Strength of Some Thawed Permafrost Sols contained the accompanying data on the following. y-shear strength of sandy) -depth (m) The predicted values and residuals were computed using the estimated regression equation 9-145.41-14.24, 12.70, +0.079,-0.236+0.441 14.7 9.0 31.6 23.83 48.0 36.5 27.1 25.6 36.7 25.8 10.0 6.0 39.2 —— 16.0 7.0 39.3 14.57 - 16.8 7.0 36.4 16.88 20.7 7.4 34.0 38.8 8.3 33.7 16.9 6.4 28.0 ** Predicted y Residual -9.13 27.0 8.1 33.0 16.0 4.6 26.4 24.9 9.8 37.9 7.3 2.8 34.5 B 12.8 1.9 36.3 SSResid SSRegr The value The value 26.46 10.77 The value The value 23.38 25.07 16.23 S 24.31 15.06 28.64 AM 15.08 15.04 8.15 0.93 -0.86 -0.77 1.43 -0.06 13.73 0.67 2.00 (4) Use the given information to calculate SSResid, SST, and SSReg (Round your answers to four decimal places) SST-X 0.94 -3.74 -7.76 -7371 4.65 (0) Calculate for this regression model. (Round your answer to three decimal places) R²-[ x How would you interpret this value? gives the percentage of observed variation in water content that can be explained by the fitted model. gives the percentage of observed variation in shear strength of sandy soll that can be explained by the fitted model gives the percentage of water content values in the sample that are equal to the values predicted by the model gives the percentage of shear strength of sandy soll values in the sample that are equal to the values predicted by the model () Use the value of R² from part (b) and a 0.05 level of significance to carry out a model utility test. Calculate the test statistic. (Round your answer to two decimal places) Use technology to calculate the value. (Round your answer to four decimal places) P-value- What can you condude? Fall to reject H. We have convincing evidence that the multiple regression model is useful. Reject H. We do not have convincing evidence that the multiple regression model is useful Reject H. We have convincing evidence that the multiple regression model is usefu Fall to reject H. We do not have convincing evidence that the multiple regression model is useful. ✓