1.1. The table below shows the hydrocarbon emissions, $x$, and the oxides of nitrogen, $y,$ for ten randomly selected cars from London with known values of $x$ and $y$, taken from the large data set.

Use your knowledge of the large data set to:

(i) state the units of both $x$ and $y$.

(ii) write down the most likely propulsion type for the two cars with hydrocarbon emissions of 0.013.

1.2. The product moment correlation coefficient between the two variables is calculated to be $r=0.7544$. The critical value for a sample size of 10 at the 0.5% level of significance is 0.7646.

(i) State suitable null and alternative hypotheses to test whether there is evidence of positive correlation between $x$ and $y$.

(ii) Test, at the 0.5% level of significance, whether there is evidence of a positive correlation between hydrocarbon emissions and oxides of nitrogen.

1.3. The linear regression line of $y$ on $x$ is given as $y=0.7433x-0.006357$.

Give an interpretation of the value 0.7433 in the context of the question.