An Investigation of the Relationship Between Traffic Flow X (1000's $\mu g / g$

Essay

An investigation of the relationship between traffic flow x (1000's of cars per 24 hours) and lead content y bark on trees near the highway ( $\mu g / g$ dry wt) yielded the data in the accompanying table. $$\begin{array} { l c c c c c c c c c c c } \hline x & 8.3 & 8.3 & 12.1 & 12.1 & 17.0 & 17.0 & 17.0 & 24.3 & 24.3 & 24.3 & 33.6 \\\hline y & 227 & 312 & 362 & 521 & 640 & 539 & 728 & 945 & 738 & 759 & 1263 \\\hline\end{array}$$ The summary statistics are: $n=11, \sum x_{i}=198.3, \sum y_{i}=7034$
, $\sum x _ { i } ^ { 2 } = 4198.03 , \sum y _ {i } ^ { 2 } = 5,390,382 , \sum x _ { i } y _ { i } = 149,354.4$ In addition, the least squares estimates are given by: $\hat { \beta } _ { 0 } = - 12.84159 \text {, and } \hat { \beta } _ { 1 } = 36.18385$ Carry out the model utility test using the ANOVA approach for the traffic flow/lead-content data of Example 12.6. Verify that it gives a result equivalent to that of the t test.