Unit Plan

## Line of Best Fit

• Assessment Anchors
• Eligible Content
• Big Ideas
• Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
• Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
• Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
• Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
• Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
• There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
• Concepts
• Algebraic properties and processes
• Analysis of one and two variable (univariate and bivariate) data
• Functions and multiple representations
• Linear relationships: Equation and inequalities in one and two variables
• Linear system of equations and inequalities
• Polynomial functions and equations
• Competencies
• Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems.
• Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
• Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.
• Write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities.

### Objectives

In this unit, students understand how variables relate to one another. Students will:

• categorize scatter plots by their correlation.
• create scatter plots.
• draw lines of best fit and write the equations of lines of best fit.
• make predictions using the line of best fit.

#### Essential Questions

• How can we determine if two variables correlate linearly?
• How can we use data to make predictions about the future?

### Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

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# Multiple-Choice Items

1. What type of correlation does the following graph have?

 A positive linear correlation B negative linear correlation C no correlation D nonlinear correlation

2. Which of the following does not have negative correlation?

 A number of hours watching TV per week versus grade-point average B car weight versus miles per gallon C height versus weight D price of an item versus number of people who want it

# 3. The scatter plot has what type of correlation?

 A nonlinear correlation B no correlation C negative linear correlation D positive linear correlation

4. The equation for the line of best fit is written in what form?

 A slope-intercept form B standard form C point-slope form D vertex form

5. In the Stroop Lab, what does the slope represent?

 A number of words in the list B color of the word C number of correct matches D seconds per word

6. Which equation best represents the line of best fit for the following scatter plot?

 A y = x + 50 B y = −50x + 1 C y = −x + 50 D y = x – 50

7. Equations of lines of best fit are used for what?

 A to tell stories B to make predictions C to draw graphs D to prove correlation

8. The line of best fit for time versus the cost of a gallon of milk is y = .02x + .10 where x represents the number of years after 1930 and y represents cost. What was the cost of a gallon of milk in 1970?

 A \$0.90 B \$39.50 C \$1.50 D \$4.80

9. The line of best fit for time versus the cost of a gallon of milk is y = .02x + .10 where x represents the number of years after 1930 and y represents cost. In what year was milk \$1.20 per gallon?

 A 1940 B 1955 C 1985 D 1995

 1. A 2. C 3. B 4. A 5. D 6. C 7. B 8. A 9. C

10.  Graph a scatter plot that has a negative correlation.

11.  The line of best fit is drawn in the scatter plot. What is the equation of the line of best fit?

12.  Plot the following data, draw a line of best fit, and write the equation of the line of best fit.

 x 0 1 2 3 4 5 6 7 10 y 2 5 9 10 14 19 21 25 30

# Short-Answer Key and Scoring Rubrics:

10.  Graph a scatter plot that has a negative correlation.

11.  The line of best fit is drawn in the scatter plot. What is the equation of the line of best fit?

y = (7/6)x

12.  Plot the following data, draw a line of best fit, and write the equation of the line of best fit.

 x 0 1 2 3 4 5 6 7 10 y 2 5 9 10 14 19 21 25 30

y = 2.954x + 2.528 (from calc)

 Points Description 3 ·         An accurate line of best fit has been drawn on a scatter plot with axes labeled. ·         An accurate equation for the line of best fit has been provided. 2 ·         The scatter plot is made and there is a line of best fit but no equation. 1 ·         The line of best fit equation is provided, but there is no scatter plot or line of best fit drawn. 0 ·         The student’s response is incorrect, irrelevant, too brief to evaluate, or missing.

# Performance Assessment:

Research and find two variables that have linear correlation.

1. Make a table of values with your data.

2. Make a scatter plot of your data and label the axes.

3. Draw in a line of best fit.

4. Write the equation of the line of best fit:

5. What does the slope represent in terms of your data?

6. What does the y-intercept represent in terms of your data?

7. Using your line of best fit, write one question in which you have to solve for y. Show the answer.

8. Using your line of best fit, write one question in which you have to solve for x. Show the answer.

# Performance Assessment Scoring Rubric:

 Points Description 5 The student has the following: ·         a table with data that correlates linearly ·         a scatter plot with axes labeled ·         a graph of the line of best fit ·         the equation of the line of best fit ·         a proper explanation of the slope ·         a proper explanation of the y-intercept ·         one question and answer in which solving for y ·         one question and answer in which solving for x 4 The student has the following: ·         a table with data that correlates linearly ·         a scatter plot, but axes are not labeled ·         a graph of the line of best fit ·         the equation of the line of best fit ·         a proper explanation of the slope ·         a proper explanation of the y-intercept ·         one question and answer in which solving for y ·         one question and answer in which solving for x 3 The student has the following: ·         a table with data that correlates linearly ·         a scatter plot, but axes are not labeled ·         the equation of the line of best fit, but not its graph ·         a proper explanation of the slope ·         a proper explanation of the y-intercept ·         one question and answer in which solving for y ·         one question and answer in which solving for x 2 The student has the following: ·         a table with data that correlates linearly ·         the equation of the line of best fit ·         incorrect explanations of slope and y-intercept ·         one question and answer in which solving for y ·         one question and answer in which solving for x 1 The student has the following: ·         a table with data that correlates linearly ·         the equation of the line of best fit ·         incorrect explanations of slope and y-intercept ·         one question but missing the answer in which solving for y ·         one question but missing the answer in which solving for x 0 The student’s response is incorrect, irrelevant, too brief to evaluate, or missing.

DRAFT 11/03/2010