# Linear Regression and Correlation

This is an activity/Lesson Plan from Shodor on developing a scatterplot and determining the correlation of the data.  This has discussion questions and activities for demonstrating and understanding the correlation coefficient.  This includes handouts and extensions of the activity as well as adaptations for differentiated instruction. This activity gives the needed vocabulary for linear functions and scatterplots. The students will develop a scatterplot and look at the correlation of the data. It explains the correlation coefficient and a has a regression activity. It has handouts included that can be downloaded and printed for the students.

### Standards & Objectives

CCSS.Math.Content.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
CCSS.Math.Content.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive...
CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
CCSS.Math.Content.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe...
CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For...
GLE 0806.3.4
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
GLE 0806.5.2
Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
SPI 0806.3.4
Translate between various representations of a linear function.
SPI 0806.5.3
Generalize the relationship between two sets of data using scatterplots and lines of best fit.
TSS.Math.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in...
TSS.Math.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive...
TSS.Math.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
TSS.Math.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such...
TSS.Math.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a...

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Learning objectives:

Objectives

Upon completion of this lesson, students will:

• have plotted bivariate data onto a scatter plot
• have seen the line of best fit for several different scatter plots
• be able to estimate the lines of best fit for data sets
• be able to estimate the correlation coefficient for data sets

### Lesson Variations

Blooms taxonomy level:
Understanding
Differentiation suggestions:

Alternate Outline:

This lesson can be rearranged in several ways.

• omit the discussion of the correlation coefficient
• omit the scatter plot worksheet
• As a class, before splitting them into groups, have the students plot specific points on the Regression activity and have each of them draw the line of best fit that they imagine. Then, have them select the true line of best fit and see who had the closest estimation.