IRTVD - Interpreting and Representing Two Variable Data (Overview)

Interpreting and Representing Two Variable Data

Introduction

Now that you understand how to compare one-variable data, let's look at data sets with two variables. For instance, you are collecting data on how many hours you spend studying for a test and your score on the test. You can plot and analyze that data to decide what amount of study time would give you the best results on your test. How cool is that?! 

Essential Questions

1. How do I summarize, represent, and interpret data on two categorical and quantitative variables?
2. How do I interpret relative frequencies in the context of a two-way frequency table?
3. Why is technology valuable when making statistical models?
4. How do you determine the regression line or line of best fit for a scatter plot of data?
5. Why are linear models used to study many important real-world phenomena?
6. How do I interpret linear models?
7. How do I determine if linear or exponential regression is more appropriate for a scatter plot?
8. How can I apply what I have learned about statistics to summarize and analyze real data?

Key Terms

The following key terms will help you understand the content in this module.

Association - A connection between data values.

Bivariate data - Pairs of linked numerical observations. An example would be to lists the heights and weights for each player on a football team.

Conditional frequencies - The relative frequencies in the body of a two-way frequency table.

Correlation coefficient - A measure of the strength of the linear relationship between two variables that is defined in terms of the (sample) covariance of the variables divided by their (sample) standard deviations.

Joint frequencies - Entries in the body of a two-way frequency table.

Line of Best Fit (trend or regression line) - A straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. An exponential model will produce a curved fit.

Marginal frequencies - Entries in the body of a two-way frequency table.

Relative Frequency Table - Displays frequency counts as a proportion of the total.

Scatter plot - A straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. An exponential model will produce a curved fit.

Trend - Displays frequency counts as a proportion of the total.

Two-Way frequency table - A useful tool for examining relationships between categorical variables. The entries in the cells of a two-way table can be frequency counts or relative frequencies.

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