1.1. On 21^st January 2020, doctors in China started recording and reporting the number of new daily cases of an unknown virus. The table below shows the number of new cases, $c$, of the virus in China for each day, $d$, after 21^st January 2020.

The value of the product moment correlation coefficient between the number of days after 21^st January 2020 and the number of new cases was calculated as $r=0.900$.

The table below gives the critical values, for different significance levels, of the product moment correlation coefficient, $r$, for a sample size of 12.

(i) Clearly stating suitable null and alternative hypotheses, show that there is evidence of linear correlation between the number of days and the number of new cases at a 1% level of significance.

(ii) Give a reason why a linear regression line is suitable to model the relationship between the number of days and the number of new cases reported each day.

1.2. The equation for the regression line of $c$ on $d$ is found to be $c=185d-266.$

(i) Interpret the value of 185 in context.

(ii) Explain why the equation for the regression line should not be used to estimate how many new cases there were on 19^th January 2020.