Each day a supermarket records the midday temperature and how many cold drinks are sold on that day. The following table shows the supermarket’s data for the last 6 days. This data is also shown on a scatter diagram.

Write down

i)     the mean temperature, \({\bar x}\) ;

ii)    the mean number of cold drinks sold, \({\bar y}\) .

Draw the line of best fit on the scatter diagram.

Use the line of best fit to estimate the number of cold drinks that are sold on a day when the midday temperature is \(10\,^\circ {\text{C}}\).

i)     \(14\)         (A1)

ii)    \(380\)         (A1)    (C2)

(A1)(ft)(A1)   (C2)

Note: Award (A1)(ft) for a straight line going through their mean point, (A1) for intercepting the y-axis between \(160\) and \(220\) inclusive. Follow through from part (a).

an attempt to use their line of best fit to find \(y\) value at \(x = 10\)               (M1)

Note: Award (M1) for an indication of use of their line of best fit (dotted lines or some indication of mark in the correct place on graph).

OR

\(13.4\,(10) + 192\)               (M1)

Note: Award (M1) for correct substitution into the regression equation, \(y = 13.4x + 192\).

\( = 326\)               (A1)(ft)     (C2)

Note: Follow through from part (b). Accept answers between \(310\) and \(340\), inclusive.

Question 9: Linear regression.

The correct means were usually written down. Many candidates drew a line of best fit that did not go through their \((\bar x,\,\,\bar y)\). Almost all candidates were able to use the line of best fit (either the one they had drawn or the regression line found using their GDC) to make a reasonable estimate. Feedback from teachers suggests that many are using line of best fit and line of regression as synonyms. This is not the case; both are explicitly mentioned in the guide and candidates are expected to understand both terms.

Question 9: Linear regression.

The correct means were usually written down. Many candidates drew a line of best fit that did not go through their \((\bar x,\,\,\bar y)\). Almost all candidates were able to use the line of best fit (either the one they had drawn or the regression line found using their GDC) to make a reasonable estimate. Feedback from teachers suggests that many are using line of best fit and line of regression as synonyms. This is not the case; both are explicitly mentioned in the guide and candidates are expected to understand both terms.

Question 9: Linear regression.

The correct means were usually written down. Many candidates drew a line of best fit that did not go through their \((\bar x,\,\,\bar y)\). Almost all candidates were able to use the line of best fit (either the one they had drawn or the regression line found using their GDC) to make a reasonable estimate. Feedback from teachers suggests that many are using line of best fit and line of regression as synonyms. This is not the case; both are explicitly mentioned in the guide and candidates are expected to understand both terms.