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.