Regression Models Answers

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constant additive rate of change✔ constant multiplicative rate of changedistinct turning point

A
constant additive rate of change
B
constant multiplicative rate of change
C
distinct turning point
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✔ exponentialquadraticlinear

A
exponential
B
quadratic
C
linear
5

Which quadratic model best represents the data?

A
f(x) = –16x2 + 99x + 6
B
f(x) = –36x2 + 37x + 5
C
f(x) = 36x2 + 37x + 5
D
f(x) = 16x2 + 99x + 6
8

Which statements are true? Check all that apply.

A
The data is best represented by an exponential model.
B
The data is best represented by a quadratic model.
C
If the price is $5 per unit, the expected profit is approximately $4,686.
D
If the price is $80 per unit, the expected profit is negative.
E
As the price per unit increases, the profit increases indefinitely.
9

Which statements are true? Check all that apply.

A
The function that best represents the data is f(x) = 24,512(0.755)x.
B
The function that best represents the data is f(x) = 554x2 – 5,439x + 24,600.
C
The function decreases indefinitely.
D
It is reasonable to interpolate to the value of the car at 4.5 years.
E
It is reasonable to extrapolate to 40 years.
12

Charlie used a regression calculator to generate the equation f(x) = –0.15x + 20.1 for the ordered pairs (2, 15), (4, 21), (6, 26), (8, 20), and (10, 14).Is a linear representation the best way to represent the data? If it is, explain why. If not, explain why and suggest a better alternative.

Answer:

The rvalue for the linear function related to the ordered pairs is very close to zero, so it is not a good representation of the data. A quadratic model would better represent the data because there is a turning point within the data set. The data increases then decreases, which is what the graph of a quadratic does.

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What did you include in your response? Check all that apply.

A
The linear function does not represent the data well.
B
The r-value for the linear model is close to zero.
C
The graph increases then decreases, or has a turning point.
D
A quadratic model better represents the data.
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