2.29, revised
During a recent solar car race, you gathered data on daily power consumption and total mileage traveled.
Let n denote the number of data points collected. For example, you may have collected the following data
with n = 5:
Power consumed
10
8
13
15
9
Distance
60
55
75
81
62
There is believed to be a linear relationship between power and distance, that is, of the form:
distance = m(power) + b,
for some unknown values of m and b, along with some random error term. In a statistics class, you would
generate a least-squares regression line that minimizes the sum of squared difference between the observed
distances and the predicted distances, based on the linear model, that is,
min
n
X
(distancek − (m · powerk + b))2 .
k=1
Suppose instead you want to minimize the sum of the absolute deviations between the observed and predicted
distances, that is,
n
X
|distancek − (m · powerk + b)|.
min
k=1
What values of m and b will give this? Note that both m and b should be nonnegative.
1