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# A2-D-1-2

last edited by 5 years, 1 month ago

A2.D.1.2 Collect data and use scatterplots to analyze patterns and describe linear, exponential or quadratic relationships between two variables. Using graphing calculators or other appropriate technology, determine regression equation and correlation coefficients; use regression equations to make predictions and correlation coefficients to assess the reliability of those predictions.

In a Nutshell

Students will gather data from a specific real-world scenario, identify the dependent and independent variable and create a scatter plot.  From the scatter plot, they will identify the correct shape of the data and calculate a line or quadratic regression as appropriate.  The correlation coefficient from that regression will allow students to correctly assess the reliability of any future prediction derived from the line/curve of best fit.

## Teacher Actions

• Students will generalize and identify patterns within scatter plots and make conjectures to identify the line/curve of best fit.

• Students will communicate  a mathematical explanation of the correlation coefficient of various data sets and how it measures the strength between the line/curve of best fit and its scatter plot.

• Students will make conjectures using the correlation coefficient of a given regression, make future predictions and assess the reliability of those predictions.

• Use and connect mathematical representations by selecting different types of data collection which should yield different scatter plots to allow students to decide which representation to use when finding the line/curve of best fit.

• Pose purposeful questions that allow students to discuss and explain how the correlation coefficient can measure the correlation between a line/curve of best fit and its scatter plot.

• Support productive struggle in learning mathematics by asking questions that go beyond gathering information to probe thinking and require explanation and justification of any future prediction of a data set with a specific correlation coefficient.

• Provide activities for students to investigate using various tools such as technology (desmos, graphing calculator, etc.). Allow time for students to collaborate, discuss and defend their findings and generalizations.

## Misconceptions

• Gather data from a real-world situation to create a scatter plot and find the line/curve of best fit.
• Identify the dependent and independent variable within a real-world situation.
• Identify the correlation coefficient as the measures of the correlation strength between the line of best fit and the scatter plot.
• Understand that a correlation coefficient values are from -1 to 1 where 0 indicates no correlation and 1 indicates a perfect positive correlation and -1 indicates a negative correlation between the line of best fit and its scatter plot.

• Students have a hard time identifying the dependent and independent variable.
• Students mistakenly try to use just a few of the points on one side of the data that may look linear when in reality the data may be parabolic in shape and a linear regression function will not accurately model this data.
• Students sometimes confuse the correlation coefficient with the slope of the regression line.

• Students struggle extracting information from the graph.

OKMath Framework Introduction