Question

I need help clarifying some answers I have for these two different questions. For the first section, should I write A to B as (4,1) and (5,10) for G to H too?
And how do I write the linear regression for the second section? I have -.005 x 47.78 as the equation...

Answer 1

Step-by-step explanation:

1a) The rate of change is the slope of the segment.

From A to B:

m = (4 mi − 0 mi) / (1 hr − 0 hr)

m = 4 mi/hr

From G to H:

m = (0 mi − 5 mi) / (10 hr − 8 hr)

m = -2.5 mi/hr

1b) From A to B, the distance is increasing, so the hiker is moving away from his home.

1c) The hiker was gone from home for 10 hours.

1d) The distance the hiker hikes is:

d = 4 mi + 2 mi + 0 mi + 2 mi + 1 mi + 0 mi + 5 mi

d = 14 mi

2a) As you found, the equation of the linear regression line is:

y = -0.005x + 47.78

2b) If the weight is 3500 lb, the expected fuel mileage is:

y = -0.005(3500) + 47.78

y = 30.28

2c) You can use Excel or a graphing calculator to find the correlation coefficient r², or you can calculate r manually:

r = ∑[(x − μₓ)(y − μᵧ)] / (sₓ sᵧ (n − 1))

where x is the weight, y is the mileage, μₓ is the average weight, μᵧ is the average mileage, sₓ is the standard deviation of the weights, sᵧ is the standard deviation of the mileages, and n is the number of data points.

μₓ = 3390, sₓ = 30.3

μᵧ = 842, sᵧ = 4.90

n = 9

r = (-29200) / (30.3 × 4.90 × (9 − 1))

r = -0.8848

r² = 0.7829