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A study was performed to investigate the shear strength of
Chapter 12, Problem 5E(choose chapter or problem)
A study was performed to investigate the shear strength of soil \(\text { (y) }\) as it related to depth in feet \(\left(x_{1}\right)\) and percent of moisture content \(\left(\mathrm{x}_{2}\right)\). Ten observations were collected, and the following
\(\text { summary quantities obtained } n=10\)
\(\Sigma x_{i 1}=223, \Sigma x_{i 2}=553\)
\(\Sigma x_{i 2}^{2}=31,729, \Sigma x_{i 1} x_{i 2}=12,352\)
\(\Sigma x_{i 1} y_{i}=43,550.8, \Sigma x_{i 2} y_{i}=104,736.8 \text { and } \Sigma y_{i}^{2}=371,595.6\)
\(Y=\beta_{0}+\beta_{1}+x_{1}+\beta_{2} x_{2}+\epsilon\)
\(x_{1}=18\)
\(x_{2}=43 \%\)
Set up the least squares normal equations for the model \(Y=\beta_{0}+\beta_{1}+X_{1}+\beta_{2} X_{2}+\epsilon\).Estimate the parameters in the model in part (a).What is the predicted strength when \(\mathrm{x}_{1}=18\) feet and \(\mathrm{x}_{2}=43 \%\)?
Equation Transcription:
Text Transcription:
(y)
(x1)
(x2)
summary quantities obtained n=10
Sigma x_i 1=223, \Sigma x_i 2=553
Sigma x_i 2^2=31,729, \Sigma x_i 1 x_i 2=12,352
Sigma x_i 1 y_i=43,550.8, \Sigma x_i 2 y_i=104,736.8 and \Sigma y_i^2=371,595.6
Y=\beta_0+\beta_1+x_1+\beta_2 x_2+\epsilon
x_{1}=18
x_{2}=43 \%
Questions & Answers
QUESTION:
A study was performed to investigate the shear strength of soil \(\text { (y) }\) as it related to depth in feet \(\left(x_{1}\right)\) and percent of moisture content \(\left(\mathrm{x}_{2}\right)\). Ten observations were collected, and the following
\(\text { summary quantities obtained } n=10\)
\(\Sigma x_{i 1}=223, \Sigma x_{i 2}=553\)
\(\Sigma x_{i 2}^{2}=31,729, \Sigma x_{i 1} x_{i 2}=12,352\)
\(\Sigma x_{i 1} y_{i}=43,550.8, \Sigma x_{i 2} y_{i}=104,736.8 \text { and } \Sigma y_{i}^{2}=371,595.6\)
\(Y=\beta_{0}+\beta_{1}+x_{1}+\beta_{2} x_{2}+\epsilon\)
\(x_{1}=18\)
\(x_{2}=43 \%\)
Set up the least squares normal equations for the model \(Y=\beta_{0}+\beta_{1}+X_{1}+\beta_{2} X_{2}+\epsilon\).Estimate the parameters in the model in part (a).What is the predicted strength when \(\mathrm{x}_{1}=18\) feet and \(\mathrm{x}_{2}=43 \%\)?
Equation Transcription:
Text Transcription:
(y)
(x1)
(x2)
summary quantities obtained n=10
Sigma x_i 1=223, \Sigma x_i 2=553
Sigma x_i 2^2=31,729, \Sigma x_i 1 x_i 2=12,352
Sigma x_i 1 y_i=43,550.8, \Sigma x_i 2 y_i=104,736.8 and \Sigma y_i^2=371,595.6
Y=\beta_0+\beta_1+x_1+\beta_2 x_2+\epsilon
x_{1}=18
x_{2}=43 \%
ANSWER:
Step 1 of 3
Given that,
The regression model with n observations and k independent variables is,
The summary statistics is,
