2013 H2 Mathematics Paper 2 Question 10

Linear Correlation and Regression

Answers

Case (A) is most appropriate as the scatter diagram in (ii) looks closest to the sketch for (A) in (i), with

{y}

decreasing at an increasing rate as

{x}

increases.

{r=-0.939}

{y = 190-0.00462x^2}

Distance travelled

{=134 \textrm{ km}}

Case (A) is most appropriate as the scatter diagram in (ii) looks closest to the sketch for (A) in (i), with

{y}

decreasing at an increasing rate as

{x}

increases.

r=-0.939 \textrm{ (3 sf)} \;\blacksquare

Using a GC, least squares regression line of

{y }

{x^2:}

\begin{align*} & y = 189.75-0.0046198x^2 \\ & y = 190-0.00462x^2 \textrm{ (3 sf)} \; \blacksquare \end{align*}

When

{x=110,}

\begin{align*} & \textrm{Estimated distance travelled} \\ &= 189.75 -0.0046198 (110)^2 \\ &= 134 \textrm{ km (3 sf)} \; \blacksquare \end{align*}