Free Practice Quiz Question List

11 Mathematical Modeling Online Quiz Questions

Use this free practice quiz with 20 questions to review 11 Mathematical Modeling, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A quantity has values near 200, 220, 242, and 266.2 at equally spaced times. Which model type is most plausible, and why?

A
A linear model, because the values increase by about the same additive amount each period.
B
An exponential model, because the values increase by about the same percentage each period.
C
A constant model, because the output remains approximately unchanged.
D
A sinusoidal model, because the values repeat in a regular cycle.

Choose one

1 point

For one observation, the observed value is $y_i=145$ and the model predicts $\hat y_i=152$ . Which statement correctly gives the residual and its interpretation?

A
$-7$ , so the model underpredicted by 7 units
B
$7$ , so the model overpredicted by 7 units
C
$-7$ , so the model overpredicted by 7 units
D
$7$ , so the model underpredicted by 7 units

Choose one

1 point

A function models the population of a town as a function of elapsed time since a study began. Which domain choice is most defensible?

A
Restrict the domain to nonnegative times.
B
Allow every real number because functions always have real-number domains.
C
Use only negative times to avoid extrapolation.
D
Set the domain equal to the possible output values.

Choose all

1 point

Which two features would support the adequacy of a fitted model in a residual analysis? Select all correct choices.

A
Residuals are generally scattered around zero.
B
Residuals form a clear U-shaped curve.
C
The vertical spread is reasonably similar across the prediction range.
D
Residuals form a steadily increasing run over time.

Choose all

1 point

Which two questions are appropriate when validating a mathematical model? Select all correct choices.

A
Whether the data are representative of the situation being modeled
B
Whether the model has the largest possible number of parameters
C
Whether important variables may have been omitted
D
Whether the fitted curve passes through every observed point

True or false

1 point

True or false: A positive residual means that the model underpredicted the observed response.

A
True
B
False

True or false

1 point

True or false: If two variables are strongly associated in a data set, the association by itself proves that one variable causes the other.

A
True
B
False

Written response

1 point

A fitted model for monthly electricity use is $\hat E=18T+420$ , where $T$ is average temperature in degrees Celsius and $\hat E$ is measured in kilowatt-hours. What value does the model predict when $T=12$ ?

Written response

1 point

What is the modeling term for estimating a response at an input value that lies inside the range of observed inputs?

Fill in the blank

1 point

Complete both statements about the fitted line $\hat y=mx+b$ : The slope $m$ has units of , and the intercept $b$ represents the when that input is meaningful.

Fill in the blank

1 point

Complete both statements: To make fitting an exponential model $y=ab^x$ approximately linear, take the of $y$ . This method requires response values.

Open ended

1 point

For the exponential model $P(t)=P_0b^t$ , explain the meanings of $P_0$ and $b$ , and describe how the value of $b$ determines growth or decay. Include the formula for the percent change per time unit.

Choose one

1 point

A quadratic model for weekly sales is $\hat y=-0.04x^2+1.8x+12$ , where $x$ is advertising spending in hundreds of dollars. At which advertising input does the model predict its maximum sales?

A
$x=18$
B
$x=20$
C
$x=22.5$
D
$x=45$

Choose one

1 point

A quantity has values near 100, 110, 121, and 133.1 at equally spaced times. Which model is most appropriate for this pattern?

A
A linear model, because the values increase
B
An exponential model, because the ratios are approximately constant
C
A quadratic model, because the values are not identical
D
A constant model, because all values are near 100

Written response

1 point

A fitted model for monthly electricity use is $\hat E=18T+420$ , where $T$ is average temperature in degrees Celsius and $\hat E$ is measured in kilowatt-hours. What value of $\hat E$ does the model predict when $T=12$ ?

True or false

1 point

True or false: If a residual is positive, the fitted model underpredicted the observed response.

A
True
B
False

Written response

1 point

What is the modeling term for estimating a response at an input value inside the range of observed inputs?

Choose one

1 point

A residual plot from a fitted linear model shows a clear curved pattern rather than random scatter around zero. What is the most appropriate conclusion?

A
The linear model is necessarily causal
B
The measurements must all be correct
C
The linear model may be missing curvature
D
The response has no variation

Choose one

1 point

Why does least-squares fitting minimize the sum of squared residuals instead of the unsquared residuals?

A
It guarantees that every prediction equals an observation
B
It prevents cancellation of opposite-signed errors and emphasizes larger errors
C
It removes the need to inspect residual plots
D
It makes the fitted model causal

Choose one

1 point

A fitted advertising-sales model is $\hat y=-0.04x^2+1.8x+12$ . At what advertising input $x$ does this quadratic model reach its maximum predicted sales?

A
$x=-22.5$
B
$x=0.04$
C
$x=22.5$
D
$x=45$