Name_________________________________________________ Date_______________ Period________
4.1.2-How Close is the Model?
To determine if the line of best fit is a good model for the data, we can look at the residuals, which is the
difference between the observed value (the data) and the predicted value (the y-value on the regression line).
1. The residuals are the lengths of the segments. How can you calculate the length of the segment to get the
residual?
2. If the data point is above the best fit line, the residual is positive. If the point is below the best fit line, it is
negative. Fill in the table below with the positive and negative residual values.
x
1
2
3
4
5
6
y
10
13
7
22
28
19
Residual Value
3. You are trying to help a cereal company determine the best type of box for specific amounts of cereal. Below
is a list of data for six current packages. Make a scatter plot using this data.
Packaging
Cardboard (in​2​) - x
34
150
218
325
357
471
Net Weight of
Cereal (g) - y
21
198
283
567
680
1020
​
​
a.​ Construct a ​line of best fit to model this
data. A line of best fit is a line we draw to fit
our data as accurately as possible. They
key is not to hit as many points as possible,
but to get as close to as many points as
possible.
b.​ Now write an equation for your line for
best fit. This is a ​function to model your
data. Then use your function to e
​ stimate
the net weight of cereal in a box that has
260 in​2​ of packaging cardboard.
c.​ A ​residual is a measure of how far a prediction is from what is actually observed.
residual = actual data − predicted data
Actual data: scatter plot
Estimated data: line of best fit
What is the residual of your graph for the box with 260 in2 of packaging cardboard if the actual net weight of
cereal is 355g? Is this a positive or a negative residual?
4. This is a table describing how much money a waiter earned hourly:
x
Hours worked
0
3
6
9
12
15
18
21
y
Dollars earned
0
15
68
95
150
155
210
200
Construct a scatter plot and a line of best fit. Then,
use your line of best fit to construct an equation.
Without calculating, Which points appear to have
positive residuals? How do you know?
Without calculating, Which points appear to have
negative residuals? How do you know?
5. Simplify the given polynomials:
1. y = x(x-5)
2. y = (2x-4)(5x+10)
3. y = (x+4)(2x-7)
4. y = (2x2 + x + 4)(2x − 4)
6. Simplify the following exponential expressions:
x−5
(x2 )5
x5 x3
x7
x3