# 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.9  The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic and exponential functions.

Bloom's Level:  Evaluate

### 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) = anxn + an-1xn-1 +...+ a1x + a0, where n is a nonnegative integer, and the coefficients are real numbers), exponential (y = bx), and logarithmic (y = logbx) models arise from real-world situations.

·  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

All.91  Collect and analyze data.

All.92  Investigate scatterplots to determine if patterns exist and then identify the patterns

All.93  Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, and logarithmic functions.

·  AII.91  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.94  Make predictions, using data, scatterplots, or the equation of the curve of best fit.

·  AII.92  Make predictions, using data, scatterplots, or the equation of the curve of best fit.

All.95  Given a set of data, determine the model that would best describe the data.

·  AII.93  Solve practical problems involving an equation of the curve of best fit.

·  AII.94  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