Consider the following table, which shows a data set relating the number of full days hikers spent on the Appalachian trail (a very long trail that attracts ambitious hikers), and the number of miles they hiked along the trail.
x (full days of hiking) y (miles hiked)
3 49
1 13
6 88
8 107
2 33
11 177
9 138
88 1496
7 111
33 488
51 852
13 198
To check this is entered correctly on your calculator, press [stat], go to CALC, and select "2:2-Var Stats". Run this on your two lists. When you scroll down the list, you should see Σxy=199354
Enter this data into your calculator and obtain a linear equation of best fit using the linear regression feature. Type the equation here in y=mx+b
form, rounding m
and b
to two decimal places.
Based on your regression equation above, predict how many miles a hiker would be able to hike on the Appalachian trail if they planned to hike for 36 days. Round your answer to the nearest full mile.
miles
If a typical hiker wanted to see a solid 915-mile stretch of the Appalachian Trail, how many days should they plan to hike? Round up to the next full day.
days
The linear regression equation obtained is y = 16.89x + 4.27
Predicted miles for 36 days: y = 16.89(36) + 4.27 = 611.21, rounded to the nearest full mile is 611 miles
To hike 915 miles, the hiker would need to plan for y = (915 - 4.27) / 16.89 = 53.61 days. Rounded up to the next full day, the hiker should plan to hike for 54 days.