Let us start by plotting the graph of years (x-values) and imports (y-values).
From the graph above, we can conclude that the trend appears linear. I started the year by replacing 1992 by 2yrs, 1994 by 4yrs, etc.
Therefore, the formula for the linear regression line is,
[tex]y=ax+b[/tex]
where,
[tex]\begin{gathered} a=409.503\approx409.50(nearest\text{ hundredth)} \\ b=1109.82_{_{_{_{_{_{}}}}}} \end{gathered}[/tex]
Therefore, the linear regression line is
[tex]y=409.50x+1109.82[/tex]
Now let us get the year import will exceed 12,000 by substituting the values of y to be 12,000 in the equation above.
[tex]\begin{gathered} _{_{_{_{}}}}12000=409.50x+1109.82 \\ 12000-1109.82=409.50x \\ 10890.18=409.50x \\ \frac{10890.18}{409.50}=\frac{409.50x}{409.50} \\ 26.594=x \\ \Rightarrow x=26.594\approx27(nearest\text{ whole number)} \end{gathered}[/tex]
Hence, the year in which the import will exceed 12,000 will be in the year 2017.
Finally, from the graph we find the value of r to be 0.9848.
