Researchers Wish to Study Fuel Consumption Rates Based on Speed

Essay

Researchers wish to study fuel consumption rates based on speed.The data from 10 cars are below:
$\begin{array} { | l | l | } \hline \text { Speed } & \text { Miles/Gallon } \\\hline 15 & 14 \\\hline 23 & 17 \\\hline 30 & 20 \\\hline 35 & 24 \\\hline 42 & 26 \\\hline 45 & 23 \\\hline 50 & 18 \\\hline 54 & 15 \\\hline 60 & 11 \\\hline 65 & 10 \\\hline\end{array}$
It can be shown that for these data: $\bar{X}=41.9, \quad \bar{y}=17.8, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)^{2}=2352.9$
$\sum_{i=1}^{10}\left(y_{i}-\bar{y}\right)^{2}=267.6, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=-270.2$
Calculate b₁.