2022 H2 Mathematics Paper 2 Question 10

There is a negative correlation between ${d}$ and ${p.}$ As seen by the negative value of the product moment correlation coefficient and the scatter diagram, an increase in ${d}$ is correlated with a decrease in ${p.}$

There is only a moderate linear correlation between ${d}$ and ${p}$ as indicated by the value of the product moment correlation coefficient. In the scatter diagram, it can be observed that a straight line is not the best fit for the data as the rate or decrease of ${p}$ decreases as ${d}$ increases.

The product moment correlation will stay the same as a change in units does not affect the strength of the linear correlation between ${d}$ and ${p.}$

As the special car has a bigger engine and many extra features, any possible data trend between ${d}$ and ${p}$ for the other six cars may not be applicable for this special car. Using the data relating to this special car could lead to a less accurate result with weaker correlation.

The distances are squared so that any negative values that arise from subtracting a larger value from a smaller will be made positive.

This is referred to as the "method of least squares" as the least squares regression line of ${p}$ on ${\frac{100\; 000}{d}}$ is the line such that the total squares of these distances is made the least.

${p = 506 \left( \frac{100\; 000}{d} \right) + 9400.}$
${r = 0.987.}$

${\pounds 19,400}$

I would not expect it to be reliable as ${d=5055}$ is outside the given data range from ${8954}$ to ${45 \; 452.}$ The observed data trend may no longer hold outside the given data range.