In a Study of the Factors That Affect Success in Economics,data

Essay

In a study of the factors that affect success in economics,data were collected for 8 business students.Scores on a calculus placement test are given with economics final exam scores.The data are below:
$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Calculus } \\\text { Placement Score }\end{array} & \begin{array} { l } \text { Exam Final } \\\text { Score }\end{array} \\\hline 17 & 73 \\\hline 21 & 66 \\\hline 11 & 64 \\\hline 16 & 61 \\\hline 15 & 70 \\\hline 11 & 71 \\\hline 24 & 90 \\\hline 27 & 68 \\\hline\end{array}$
It can be shown that for these data: $\bar{X}=17.75, \quad \bar{y}=70.38, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)^{2}=237.50$
$\sum_{i=1}^{8}\left(y_{i}-\bar{y}\right)^{2}=545.875, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=140.75$
Calculate b₁.