MANE 6313
Week 12, Module B
Student Learning Outcome
- Select an appropriate experimental design with one or more factors,
- Select an appropriate model with one or more factors,
- Evaluate statistical analyses of experimental designs,
- Assess the model adequacy of any experimental design, and
- Interpret model results.
Module Learning Outcome
Analyzing linear regression models.
Resources for the Week 12, Module B micro-lecture are:
Fitting Linear Regression Models
Model Assumptions and Residuals
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Least squares estimation requires that \(E(\mathbf{\varepsilon})=0\) and \(V(\mathbf{\varepsilon})=\sigma^2\) and the \(\left\{\mathbf{\varepsilon}_i\right\}\) are uncorrelated
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To perform statistical hypothesis tests, we further assume that \(\mathbf{\varepsilon}\sim \mbox{NID}(0,\sigma^2)\)
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These assumptions are validated by examining the residuals
Test for Significance of Regression
- Test for significance of regression is a test to determine if there is a linear relationship between \(y\) and a subset of the regressors
\[
\begin{aligned}
H_0:\beta_1&=&\beta_2=\cdots=\beta_k=0\\
H_a:\beta_j&\neq& 0 \mbox{ for at least one }j\end{aligned}
\]
- The test statistic is
\[
F_0=\frac{SS_R/k}{SS_E/(n-k-1)}=\frac{MS_R}{MS_E}
\]
- Reject \(H_0\) if \(F_0>F_{\alpha,k,n-k-1}\)