A small business owner (SBO) recorded the length of time, y minutes, taken to travel to work when leaving home x minutes after 7am on seven selected mornings. The results are presented as follows

x	0	10	20	30	40	50	60
y	16	27	28	39	39	48	51

• Plot the distribution of the data on a scatter diagram
• Measure the product – moment correlation coefficient and interpret the statistic.
• i. derive the least square regression function of the y on x , expressing the answer in the form
• y = a + bx
• j. depict the derived relationship from [c]i. on the graph obtained in [a].
• The SBO needs to arrive at work no later than 8:40 AM. The number of minutes by which the SBO arrives early at work, when leaving home x minutes after 7 am is denoted by Z
• deduce that z = (100-a) – (1+b) x  
• hence, estimate, to the nearest minute, the latest time that the SBO can leave home without arriving late at work.