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Predicting Outcomes Using Linear Models and Regression Analysis

This unit explores the application of linear models to make predictions based on trends in data. Students will investigate the characteristics of functions, including domain, range, intercepts, and maximum/minimum values. The concept of a "best-fitting line" will be emphasized, teaching students how to estimate using linear equations in real-life scenarios, such as sports statistics and salary predictions. The unit guides learners through the process of gathering data, graphing points, and deriving the equation of the best-fitting line for effective predictions.

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Predicting Outcomes Using Linear Models and Regression Analysis

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  1. Unit 1.8 – Predict with Linear models

  2. Unit 1 – Algebra: Linear Functions • 1.8 – Predict with Linear Models • Georgia Performance Standard: • MM1A1d– Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior

  3. Vocabulary • Best-fitting line: • The line that most closely follows a trend in data • Estimating • Using a line or its equation to approximate a value outside the range of known values • Zero of a function • f(x) = 0

  4. What does a Best-fitting line look like? • Best-fitting line: • The line that most closely follows a trend in data

  5. So what’s the deal with Linear Regression? • Linear regression is the process of finding a linear equation to describe real life situations that increase or decrease in a line. • Examples: • Home Runs • Touchdowns • Eating Contests • Annual Salary (How much you make!)

  6. How can we predict what a line (data) will look like? • Steps: • Gather data points • Graph them • Draw your "line of best fit" • Select two points on the line • Find the slope between the two points • Find where the line crosses the y-axis (b) • Use the slope and one of the points to find the equation • Once you have the equation, you can make predictions about what will happen in the future or even what happened in the past.

  7. Example: Find the equation of the best-fitting line.

  8. Example: Make a scatter plot of the data. Find the equation of the best-fitting line

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