# Question 6:

## Part (a)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $x = 1.2 + 0.2(1.4x+1.5)$ o.e. or $y = 1.4(1.2+0.2y)+1.5$ o.e. | M1 | For either equation or attempt to solve simultaneously; may be implied by $x = \frac{25}{12}$/2.08 or better or $y = \frac{53}{12}$/4.42 or better |
| $x = \frac{25}{12}$, $y = \frac{53}{12}$ | A1 A1 | For either value; for both values (may be written as coordinate). **NB** This is M1 on EPEN |

## Part (a)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\left[\sum x =\right] \frac{25}{12} \times 12 [= 25]$ | A1* | For $\frac{25}{12}\times 12$; allow use of $\sum x$ rather than $\bar{x}$; as answer given no incorrect working must be seen. **Working must be shown** |

## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\left[\sum y =\right] \frac{53}{12} \times 12 = 53$ | M1 A1ft | For $'\frac{53}{12}'\times 12$ ft their $y$ coordinate; allow use of $\sum y$ rather than $\bar{y}$; for $\sum y = 53$ or ft their $y$ coordinate $\times 12$ |
| $S_{xy} = \frac{6961}{60} - \frac{(25\times 53)}{12} = 5.6$ | M1 A1 | Use of $S_{xy} = \frac{6961}{60} - \frac{25\times'\sum y'}{12}$ ft their $\sum y$; if $\sum y$ not stated then M0; 5.6 (allow awrt 5.6) |

## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{5.6}{S_{xx}} = 1.4$ and $\frac{5.6}{S_{yy}} = 0.2$ | M1 | Any correct method to find $r$: e.g. $\frac{S_{xy}}{\sqrt{S_{xx}\times S_{yy}}}$ or $\frac{S_{xy}}{S_{xx}} = 1.4$ and $\frac{S_{xy}}{S_{yy}} = 0.2$ |
| $S_{xx} = 4$ and $S_{yy} = 28$ | A1 | cao |
| $r = \frac{5.6}{\sqrt{4\times 28}} = 0.5291...$ | M1 dA1 | Correct formula applied; awrt 0.529 |

## Question (c):

| Answer/Working | Mark | Guidance |
|---|---|---|
| For use of the gradient to find $S_{xx}$ and $S_{yy}$ ft their $S_{xy}$, or use of $\dfrac{S_{xy}}{\sqrt{\dfrac{S_{xy}}{1.4} \times \dfrac{S_{xy}}{0.2}}}$, or setting both $\dfrac{S_{xy}}{S_{xx}}$ and $\dfrac{S_{xy}}{S_{yy}}$ equal to their respective gradients | M1 | Method mark for correct approach |
| $S_{xx} = 4$ and $S_{yy} = 28$, or $\dfrac{S_{xy}}{\sqrt{1.4 \times 0.2}}$ or $\dfrac{(S_{xy})^2}{S_{xx} \times S_{yy}} = 1.4 \times 0.2$ | A1 | Correct values or equivalent expression |
| For a correct expression for $r$ ft their $S_{xy}$, $S_{xx}$ and $S_{yy}$ or $\sqrt{1.4 \times 0.2}$. If answer is incorrect then you must see their stated values substituted into a correct expression for $r$. An answer of $\dfrac{\sqrt{7}}{5}$ implies M1A1M1 only | M1 | Dependent on correct expression for $r$ |
| awrt $0.529$ | dA1 | Dependent on all previous marks being awarded |