Illuminations: Exploring Linear Data

# Exploring Linear Data

 Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.

### Learning Objectives

 Students will: construct scatterplots of two-variable data interpret individual data points and make conclusions about trends in data, especially linear relationships estimate and write equations of lines of best fit

### Materials

 Grid Paper (several sheets per student or group) Bike Weights and Jump Heights Activity Sheet Weights and Drug Doses Activity Sheet Winning Times Activity Sheet (Extension Activity) Graphing Calculators (optional)

### Assessment Options

 Assess students' thinking by their responses to the questions on the activity sheets.

### Extensions

 In the Oil Changes and Engine Repair Activity, ask students, "What is the difference between data points above the line and those below the line?" Points above the line would indicate that the actual engine repairs exceeded the amount predicted by the number of oil changes. Points below the line represent situations where the engine repairs cost less than predicted. Because the line is only a summary of the relation, just as the mean or median is a summary for a single set of data, there is a degree of variation in using the line to predict. Additional discussion could explore possible reasons, in addition to the natural variation, for this deviation from the line. Excessive engine repairs could be due to bad driving habits; lower than usual temperatures, etc. Distribute the Winning Times activity sheet. Students can interpolate by predicting what might have occurred during the war years as well as look at the danger in extrapolating. The 1988 time was 4:13. The slope is meaningful but might not remain consistent as the curve levels off. The domain and range do not include the intercepts.

### NCTM Standards and Expectations

 Algebra 6-8Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. Use graphs to analyze the nature of changes in quantities in linear relationships. Data Analysis & Probability 9-12Understand histograms, parallel box plots, and scatterplots and use them to display data. For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools.

### References

 Burrill, Gail, et al. Data Analysis and Statistics Across the Curriculum, 33-37, 39, 40. Reston, VA: NCTM, 1992.

3 periods

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