Snow Peak Rentals runs snowmobile tours in Golden, British Columbia. The owner notices
that the number of tours run in a season is related to the centimetres of snowfall. The
following table shows the historical data for the average snowfall in centimetres as well as
the number of tours run each season.
Year 2004 2005 2006 2007 2008 2009 2010 2011
Snowfall
(cm) 312 332 285 345 321 365 255 317
Number
of Tours 26 28 25 30 28 32 23 27
b. Describe the trend you see in the data. (1 mark)
c. State an appropriate domain and range for this question. (2 marks)
d. Determine the equation of the linear regression line using technology. Make sure to
round the m- and b-values to the nearest hundredth. (2 marks)
e. What do the slope and y-intercept represent in the context of this problem? (2 marks)
f. Using your equation for the best fit line, predict how many tours Snow Peak Rentals
would have if the snowfall was 300 cm. Show your workings (2 marks)
b. The trend in the data appears to show a positive correlation between snowfall and the number of tours run each season.
c. Domain: Snowfall in centimetres (0, ∞)
Range: Number of tours (0, ∞)
d. Using linear regression, we find the equation of the best fit line to be:
Number of Tours = 0.06(Snowfall) + 5.53
e. The slope (0.06) represents the increase in the number of tours for every one centimetre increase in snowfall. The y-intercept (5.53) represents the estimated number of tours run when there is zero snowfall.
f. To predict how many tours Snow Peak Rentals would have if the snowfall was 300 cm, we substitute 300 for snowfall in the equation:
Number of Tours = 0.06(300) + 5.53
Number of Tours = 18 + 5.53
Number of Tours ≈ 23.53
Therefore, if the snowfall was 300 cm, Snow Peak Rentals would be predicted to run approximately 23 tours.