Prob-Stats-Teacher-Book.pdf

# Interpret the pearson correlation coefficient

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± Interpret the Pearson Correlation Coefficient describing the strength and direction of the linear relationship between variables. ± Compute linear regression models and interpret them. ± Interpret correlation tables. Contextual Learning Objectives Using the content, students will be able to do the following: ± Create models for the relationship between the insurance claim amount for a household based on its distance from the ocean and the category of storm that hits. ± Analyze correlation tables to determine key variables related to the magnitude of insurance claims (square footage, material home is made of, elevation, etc.). ± Analyze recent trends in tropical storms and hurricanes in the U.S. Common Core State Standards for Mathematics Interpreting Categorical and Quantitative Data (S-ID) ± Summarize, represent and interpret data on two categorical and quantitative variables. ± Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 6. Fit a function to the data; use functions fitted to data to solve problems in the context of data. Use given functions or choose by the context. Emphasize linear, quadratic and exponential models. a. Informally assess the fit of a function by plotting and analyzing residuals. b. Fit a linear function for a scatterplot that suggests a linear association.

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Page 21 MODULE 4 ± Interpret linear models 7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 8. Compute (using technology) and interpret the correlation coefficient of linear fit. 9. Distinguish between correlation and causation. Materials Needed Much of the work in this module can be accomplished through the student handouts. Presentation format can vary. The lesson can be teacher directed or students can work in small groups. Although not required, students may wish to use the statistical capabilities of graphing calculator technology (TI-83/84). Students can also use statistical functions in spreadsheet programs such as Microsoft Excel. Guidelines and general instructions for using these tools are provided in the student modules in the Technology Connections section. Timing This module is designed to take 1–3 class periods depending on the depth desired. Definitions ± Scatterplot —the most common graph for looking at the relationship between two quantitative variables ± Response variable —the y-axis on a scatterplot ± Explanatory variable —the x-axis on a scatterplot ± Correlation coefficient —a measure of the strength and direction of the linear relationship between two quantitative variables ± Linear regression —a predictive model that creates a line of best fit for a set of data points ± Correlation table —a table showing the correlations between every pair of variables in a collection of variables
Page 22 MODULE 4 Discussion Question Plot each of these points [as found in the student guide] on this graph: (p. 27) 1 x x x 2 x x x 3 x x x 4 x x x 5 x x x 6 x x x 7 x x x

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