Q1. One end A of an elastic string was attached to a horizontal bar and a mass, m grams, attached to the other end B. The mass was suspended freely and allowed to settle vertically below A. The length AB, l mm, was recorded, for various masses as follows.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
M & 100 & 200 & 300 & 400 & 500 & 600 \\
\hline
L & 228 & 236 & 256 & 278 & 285 & 301 \\
\hline
\end{tabular}
a. Calculate the least squares line of regression of $l$ on $m$.
b. Give, in context, interpretations for:
\qquad i. the gradient of the line
\qquad ii. the intercept of the line
c. Estimate the length of the string when a mass of 360 grams is attached at B.
d. State a physical limitation that there might be in using your equation to estimate the length of the string when a mass of 1200 grams is attached at B.