# Bringing it all together

• Describe how two quantitative variables are related (S-ID.B.6).

• Use technology to create a line of best fit (S-ID.B.6c).

• Fit a line to given data and use it to make predictions (S-ID.B.6a).

• Interpret the coefficients of a line of best fit in the context of the data to which it is fitted (S-ID.B.7).

• Compute and interpret a correlation coefficient (S-ID.B.8).

• Understand that variables with a high correlation do not necessarily have a causal relationship (S-ID.B.9).

In this section, students use all that they have learned in this unit. They are given data or they collect it, and use technology to create the line of best fit and calculate the correlation coefficient. The final step is to analyze the situation and draw conclusions based on their findings.

## Tasks

WHAT: In this task, data about the number of coffee shops and property crimes in the county are given. Students are initially given 8 data points and must describe the relationship, compute the correlation coefficient and use it to describe and analyze the relationship between coffee shops and crime rates. In the later part of this task, students are presented with an equation for the line of best fit and must use this for further predictions. The last part of this task has students analyze and discuss (MP3) whether the data support the hypothesis that an increase in coffee shops causes an increase in crime.

WHY: This task uses many of the techniques of interpreting and analyzing bivariate data from this unit and provides a prelude to unit S4: an example of data that may be better fitted with a non-linear function than a linear one.

## External Resources

#### Description

WHAT: In this lesson, students look at data for four major pro sports leagues on various aspects of payroll (e.g., most highly paid player) and wins to answer the question: Can spending more money lead to more wins?

WHY: This lesson is placed here because it ties together all of the major components in this unit by applying them to model data (MP4) to answer a compelling question in context. Students use technology to create lines of best fit (S-ID.B.6c), compare the relative strengths of different correlation coefficients (S-ID.C.8), interpret the rate of change and constant term for lines of best fit in the context of the data (S-ID.C.7), and consider whether correlation implies causality in this situation (S-ID.C9).

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