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 43
26 372
25 350
39 593
23 386
16 221
12 204
7 134
1 20
37 596
5 71
24 334
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 Exy=87921
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 20 days. Round your answer to the nearest full mile.
miles
If a typical hiker wanted to see a solid 340-mile stretch of the Appalachian Trail, how many days should they plan to hike? Round up to the next full day.
days
The linear equation of best fit obtained from the regression on the calculator is y = 15.70x + 20.99.
If a hiker planned to hike for 20 days, the predicted number of miles they would be able to hike on the Appalachian trail is:
y = 15.70(20) + 20.99
y = 314 + 20.99
y = 334.99
Rounded to the nearest full mile, the prediction is 335 miles.
If a typical hiker wanted to see a solid 340-mile stretch of the Appalachian Trail, they should plan to hike for:
days = (340 - 20.99) / 15.70
days = 319.01 / 15.70
days ≈ 20.29
Rounded up to the next full day, they should plan to hike for 21 days.