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2.6 Competing function model validation

Worksheet
What do you remember?
1

Define the term "rate of change".

2

What are the three main types of function models?

3

What is a residual plot?

4

When might it be more appropriate to have an underestimate or overestimate for any given interval?

Let's practice
5

Given the following sets of data, identify whether a linear, quadratic, or exponential model would be most appropriate:

a
x-7-6-5-4-3-2-1
y116323611
b
x-2-50258
y140-1-4-7
c
x01234
y0-3-4-30
d
x-3-2-101\, 2\, 3
y\, \, \dfrac{1}{64}\, \, \dfrac{1}{16}\, \, \dfrac{1}{4}141664
6

Construct and plot the graph based on the following data sets.

a
x02468
y120-4012
b
x-6-4-20
y-3-2-10
c
x- 6- 4- 202
y-7595-7
d
x-3-2-10123
y\dfrac{1}{8}\dfrac{1}{4}\dfrac{1}{2}1248
e
x-3-2-10123
y8421\dfrac{1}{2}\dfrac{1}{4}\dfrac{1}{8}
f
x-10-505
y210-1
7

Given the following residuals after running a linear regression on a data set:

x-7-6-5-4-3-2-1
\text{residual}1-102-21-1

Does the linear model is a good fit? Explain.

8

A model predicted a value of 10 for a given input, but the actual value was 7. What is the error of this prediction?

9

What is the error in the model if the predicted value is 150 and the actual value is 145?

10

When would you prefer to overestimate a prediction? Provide an example.

11

When would you prefer to underestimate a prediction? Provide an example.

12

The table below shows the number of hours studied and the corresponding test scores of a group of students.

\text{Hours Studied}12345
\text{Test Score}7080889499

Can this data be modelled with a linear, quadratic, or exponential function? Justify your answer.

13

The scatter plot below shows the relationship between a car's speed and its fuel consumption.

Based on the scatter plot, would a linear, quadratic, or exponential function be most appropriate to model this data? Justify your answer.

20
40
60
80
100
120
\text{km/h}
1
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\text{Fuel Consumption}
Let's extend our thinking
14

A company is trying to predict their sales for the next year. They have data from the past 5 years. Would it be more beneficial for the company to overestimate or underestimate their sales? Explain your reasoning.

15

Consider the following data set:

x-7-6-5-4-3-2-1
y49362516941

A student claims that a linear model would be the best fit for this data. Do you agree or disagree? Justify your response.

16

Suppose a model is consistently overestimating its predictions. What kind of impact could this have in a real-world context? Provide an example to support your response.

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Outcomes

2.6.A

Construct linear, quadratic, and exponential models based on a data set.

2.6.B

Validate a model constructed from a data set.

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