2007 H2 Mathematics Paper 2 Question 11

Linear Correlation and Regression

Answers

{x = 66.2-0.260t}

{x=-11.7}

The linear model is unsuitable as it predicts a negative concentration, which is not realistic. Moreover, the scatter diagram suggests that the rate of change of

{x}

decreases on average as

{t}

increases, which is not consistent with a linear model.

(i)

{r = -0.994}

{r\approx -1,}

this indicates a strong, negative linear correlation between

{y}

and

{t.}

{r}

is closer to

{-1}

compared to

{-0.912, }

the

{\ln x = a + bt}

model is a better fit for the data compared to the linear model.

(ii)

{t = 155 \textrm{ min}}

Full solutions

Using a GC, equation of the regression line of

{x}

{t:}

\begin{align*} & x = 66.194 -0.25970 t \\ & x = 66.2-0.260t \textrm{ (3 sf)} \; \blacksquare \\ \end{align*}

When

{t=300, }

estimated value of

\begin{align*} x &= 66.194 -0.25970 (300) \\ &= -11.7 \textrm{ (3 sf)} \; \blacksquare \end{align*}