# Unit 9Modeling Data

## Lesson 1

### Learning Focus

Represent data using a scatterplot.

Understand the meaning of the correlation coefficient.

Describe the difference between correlation and causation.

### Lesson Summary

In this lesson, we have learned about representing two-variable quantitative data with a scatterplot. We have learned that one of the ways we can judge if a line is a good model for the data is by using the correlation coefficient.

## Lesson 2

### Learning Focus

Model data with a linear function.

Use a linear model to analyze data.

### Lesson Summary

In this lesson, we modeled data with linear functions. We estimated our own lines of best fit and found linear regressions using technology. We interpreted the slope and -intercept of the regression line and compared two sets of data. We learned that using the linear model to predict outcomes beyond the available data can sometimes lead to incorrect conclusions.

## Lesson 3

### Learning Focus

Interpret data using linear models.

Consider questions and necessary data for further research.

### Lesson Summary

In this lesson, we compared two sets of data to draw conclusions about men’s and women’s incomes. We interpreted the meaning of the correlation coefficients, the slope of the regression line, and intercepts of the regression line. We used the data to make claims and challenged the claims of others.

## Lesson 4

### Learning Focus

Understand and interpret residuals.

### Lesson Summary

In this lesson, we learned that a residual shows the difference between the -value of a data point and the predicted -value on the regression line. We calculated residual values and used residual plots to evaluate whether a linear model is appropriate for the data.

## Lesson 5

### Learning Focus

Clarify differences between residuals and correlation coefficients.

Use precise statistical language to discuss uses of data.

### Lesson Summary

In this lesson, we clarified the meaning of correlation coefficients and residuals and how they relate to regression lines.

## Lesson 6

### Learning Focus

Represent data with box plots, dot plots, and histograms.

Analyze data represented in different ways.

### Lesson Summary

In this lesson, we focused on single-variable quantitative data. We compared histograms, dot plots, and box plots to consider what aspects of the data are highlighted in each. We learned to look for the center, the shape, and the spread of the data.

## Lesson 7

### Learning Focus

Understand standard deviation.

### Lesson Summary

In this lesson, we learned about standard deviation, a measure of spread for single-variable quantitative data. The standard deviation is when all the data have the same value.

## Lesson 8

### Learning Focus

Compare sets of data using center, spread, and shape.

### Lesson Summary

In this lesson, we compared data distributions using shape, center, and spread. We learned to consider the interquartile range and the median when using a box plot and to consider the mean and the standard deviation when using a histogram. We also discussed the effect of outliers on the median, mean, and standard deviation.

## Lesson 9

### Learning Focus

Organize two-variable categorical data.

Interpret two-way frequency tables.

### Lesson Summary

In this lesson, we learned about two-way tables and relative frequency tables. Both types of tables are used for two-variable categorical data. Two-way tables show data counts, and relative frequency tables show percentages.