2021 H2 Mathematics Paper 2 Question 9

Linear Correlation and Regression

Answers

(a)

It is likely to provide a good model. The product moment correlation coefficient is close to

{1,}

suggesting a strong linear correlation between

{t}

and

{y.}

Moreover, the scatter diagram suggests that the rate of change of

{x}

{t}

increases is relatively constant, which is consistent with a linear model.
While relatively constant, there is still a slight increase in the rate of increase of

{x}

so there may still be a better model nevertheless

(bi)

(bii)

{c=2.29}

{d=0.0573}

{r=0.999}

(c)

The slight increase in the rate of increase of

{x}

{t}

increases indicated by the scatter diagram suggests is more consistent with the second model.

This is also shown in the product moment correlation coefficient value of

{0.999}

which is closer to

{1}

(vs

{0.9803}

for the first model), which indicates that there is a stronger linear correlation between

{\ln x}

and

{t}

as compared to the linear model.

Full solutions

(a)