#### Math - 2017-18

# AII.9 and *AII.9 - Linear and Quadratic Regressions

**AII.9** The student will **collect **and **analyze **data, **determine **the
equation of the curve of best fit, **make predictions**, and **solve **real-world
problems, using mathematical models. Mathematical models will include
polynomial, exponential, and logarithmic functions.

AII.9The student willcollectandanalyzedata,determinethe equation of the curve of best fit in order tomake predictions, andsolvepractical problems, using mathematical models of quadratic and exponential functions.

**Bloom's Level: ** Evaluate

*Adopted: 2009*

### BIG IDEAS

- I can make accurate
predictions about future events, make millions of dollars, predict the end of
the world, and always cheer for the winning team.

- I will describe relationships
between variables using graphical models, be able to predict values and
outcomes, and determine whether relationships are linear or non-linear.

### UNDERSTANDING THE STANDARD

- Data and scatterplots may indicate patterns that
can be modeled with an algebraic equation.
- Graphing calculators can be used to collect,
organize, picture, and create an algebraic model of the data.
- Data that fit polynomial (
*f(x) = a*, where_{n}x^{n}+ a_{n-1}x^{n-1}+...+ a_{1}x + a_{0}*n*is a nonnegative integer, and the coefficients are real numbers), exponential (*y = b*), and logarithmic (^{x}*y*= log) models arise from real-world situations._{b}x

· Data and scatterplots may indicate patterns that can be modeled with an algebraic equation.

· The curve of best fit for the relationship among a set of data points can be used to make predictions where appropriate.

· Knowledge of transformational graphing using parent functions can be used to verify a mathematical model from a scatterplot that approximates the data.

· Graphing utilities can be used to collect, organize, represent, and generate an equation of a curve of best fit for a set of data.

· Data that fit quadratic (), and exponential () models arise from practical situations.

· Rounding that occurs during intermediate steps of problem solving may reduce the accuracy of the final answer.

· Evaluation of the reasonableness of a mathematical model of a practical situation involves asking questions including:

“Is there another curve (quadratic or exponential) that better fits the data?”

“Does the curve of best fit make sense?”

“Could the curve of best fit be used to make reasonable predictions?”### ESSENTIALS

__Linear &
Quadratic __

All.9_{1} **Collect**
and **analyze** data.

All.9_{2} **Investigate**
scatterplots to **determine** if
patterns exist and then **identify** the
patterns

All.9_{3} **Find**
an equation for the curve of best fit for data, using a graphing calculator.
Models will include polynomial, exponential, and logarithmic functions.

· AII.9_{1} **Determine**
an equation of the curve of best fit, using a graphing utility, given a set of
no more than 20 data points in a table, graph, or practical situation.

All.9_{4} **Make**
**predictions**, using data,
scatterplots, or the equation of the curve of best fit.

· AII.9_{2} **Make
predictions**, using data, scatterplots, or the equation of the curve of best
fit.

All.9_{5} Given a set of data, **determine** the model that would best describe the data.

·
AII.9_{3} **Solve**
practical problems involving an equation of the curve of best fit.

·
AII.9_{4} **Evaluate**
the reasonableness of a mathematical model of a practical situation.

### KEY VOCABULARY

curve
of best fit, mathematical model, polynomial, exponential, logarithmic,
scatterplots, polynomial, exponential, logarithmic, predictions

*Updated: Oct 27, 2017*