The following (hypothetical) data for a city shows the relationship between the number of days with
NO rain in a year and the number of trac accidents during that year.:
DAYS WITHOUT RAIN | NUMBER OF TRAFFIC ACCIDENTS |
5 | 1008 |
15 | 943 |
30 | 902 |
40 | 804 |
50 | 798 |
In addition, the following (hypothetical) data shows the relationship between a driver's age and the
number of miles they have driven in the previous year:
DAYS WITHOUT RAIN | NUMBER OF TRAFFIC ACCIDENTS |
25 | 35000 |
30 | 33000 |
40 | 20000 |
45 | 19000 |
55 | 16000 |
(a) Use EXCEL to find the equations of the regression lines for both sets of data. Your answer
should include a plot of each regression line AND the equation of each regression line in the form
y = ax + b for appropriate constants a and b.
(b) Find the correlation coefficient, r, for both sets of data and state which data set shows the
stronger correlation.
(c) For the first data set, use the equation of the regression line to predict how many days without
rain (rounded to the nearest whole number) there would be in a year in which there were 875
traffic accidents.
(d) Use EXCEL to fit the data in the second table to an exponential model. Show the graph of the
exponential fit and give the equation.
(e) Use the exponential equation from part (d) to predict how many miles a 50 year old person would
have driven in the previous year (rounded to the nearest mile). In addition, use the exponential
equation from part (d) to predict the age of someone who has driven 25 000 miles in the previous
year (give your answer rounded to one decimal place).