Draw a scatter diagram to show the data. Use a scale of 2 cm to represent 10 metres on the x-axis and 2 cm to represent 10 plant species on the y-axis.

Using your scatter diagram, describe the correlation between the number of different plant species and the distance from the lake shore.

Use your graphic display calculator to write down \(\bar x\), the mean of the distances from the lake shore.

Use your graphic display calculator to write down \(\bar y\), the mean number of plant species.

Plot the point (\(\bar x\), \(\bar y\)) on your scatter diagram. Label this point M.

Write down the equation of the regression line y on x for the above data.

Draw the regression line y on x on your scatter diagram.

Estimate the number of plant species growing 30 metres from the lake shore.

     (A1)(A3)

Notes: Award (A1) for scales and labels (accept x/y).

Award (A3) for all points correct.

Award (A2) for 7 or 8 points correct.

Award (A1) for 5 or 6 points correct.

Award at most (A1)(A2) if points are joined up.

If axes are reversed award at most (A0)(A3)(ft).

[4 marks]

Negative     (A1)

[1 mark]

17     (G1)

[1 mark]

23     (G1)

[1 mark]

Point correctly placed and labelled M     (A1)(ft)(A1)

Note: Accept an error of ±0.5.

[2 marks]

y = –0.708x + 35.0     (G1)(G1)

Note: Award at most (G1)(G0) if y = not seen. Accept 35.

[2 marks]

Regression line drawn that passes through M and (0, 35)     (A1)(ft)(A1)(ft)

Note: Award (A1) for straight line that passes through M, (A1) for line (extrapolated if necessary) that passes through (0, 35) (accept error of ±1).

If ruler not used, award a maximum of (A1)(A0).

[2 marks]

y = –0.708(30) + 35.0     (M1)
= 14 (Accept 13)     (A1)(ft)(G2)

OR

Using graph: (M1) for some indication on graph of point, (A1)(ft) for answers. Final answer must be consistent with their graph.     (M1)(A1)(ft)(G2)

Note: The final answer must be an integer.

[2 marks]

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.

This question, by far, was the most accessible to the great majority of candidates. However, far too many candidates do not (1) use the scale as required by the question, (2) use a scale at all, (3) either draw or label axes, (4) use a ruler at all (5) use the provided graph paper. Accurate plotting of points can not be assessed unless graph paper has been used; the diagram is not a graph.

Many candidates did not seem aware that the regression line must pass through the mean point. Others, though they had obtained the equation of the regression line, did not use it to identify its y intercept.