A mathematics teacher recorded the length of time, y minutes, taken to travel to school when leaving home x minutes after 7 am on seven selected mornings. The results are as follows.

x 0 10 20 30 40 50 60

y 16 27 28 39 49 48 51

a. plot the data on scatter diagram

b. (i) calculate the equation of the least squares regression line of y on x, writing your answer in the form y = a + bc

(ii) draw the regression line on your scatter diagram

c. the mathematics teacher needs to arrive at school no later than 8.40am

the number of minutes by which the mathematics teacher arrives early at school, when leaving home x minutes after 7am, is denoted by z.

(i) decude that z = (100 – a ) – (1 +b)c

(ii) hence estimate, to the nearest minute, the latest time that the mathematics teacher can leave home without then arriving late at school