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✌️Unit 2

3 min read•june 3, 2020

Peter Cao

We can also have two sets of quantitative data to be compared as well, called a **bivariate quantitative data set**. Usually we have an **independent**, or **explanatory variable**, and a **dependent**, or **response variable**. That is, an explanatory variable explains a response to the response variable.

We can organize this data into **scatterplots**, which is a graph of the data. On the horizontal axis (also called the x-axis) is the explanatory variable and on the vertical axis is the response variable. The explanatory variable is also known as the independent variable, while the response variable is the dependent variable. Here are two examples below:

**Graph 1**

**Graph 2**

Both images courtesy of: Starnes, Daren S. and Tabor, Josh. The Practice of Statistics—For the AP Exam, 5th Edition. Cengage Publishing.

When given a scatterplot, we are often asked to describe them. In AP Statistics, there are four things graders are looking for when asked to describe a scatterplot, or describe the correlation in a scatterplot.

The **form** of a scatterplot is the general shape given by the scatterplot. This is usually either **linear** or **curved**. In the scatterplot above, Graph 1 is best described as curved, while Graph 2 is obviously linear.

The **direction** of the scatterplot is the general trend that you see when going left to right. Graph 1 is **decreasing** as the values of the response variable tend to go down from left to right while graph 2 is **increasing** as the values of the response variable tend to go up from left to right. When describing the direction for a linear model, we can refer to it as **positive **or **negative** correlation, which comes from the slope of the line that would fit the data. If the slope appears to be positive, the correlation amongst the data is also positive.

The **strength** of a scatterplot describes how closely the points fit a certain model, and it can either be **strong**, **moderate**, or **weak**. How we figure this out numerically will be on the next section about correlation and the correlation coefficient. For this, Graph 1 shows a medium strength correlation while Graph 2 shows a strong strength correlation.

Lastly, we have to discuss unusual features on a scatterplot. The two types you should know are **clusters** and **outliers**, which are similar to their single-variable counterparts.

Clusters are where points are clumped together on a scatterplot. Graph 1 has two clusters, one on the top left and the other on the top right. On the other hand, Graph 2 is more uniformly distributed.

An outlier is a point where there is a large discrepancy between the predicted response variable(y) value and the actual response variable(y) value.

Describe the scatterplot in context of the problem.

Courtesy of Starnes, Daren S. and Tabor, Josh. The Practice of Statistics—For the AP Exam, 5th Edition. Cengage Publishing.

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✍️Free Response Questions (FRQs)

👆Unit 1: Exploring One-Variable Data

✌️Unit 2: Exploring Two-Variable Data

🔎Unit 3: Collecting Data

🎲Unit 4: Probability, Random Variables, and Probability Distributions

📊Unit 5: Sampling Distributions

⚖️Unit 6: Inference for Categorical Data: Proportions

😼Unit 7: Inference for Qualitative Data: Means

✳️Unit 8: Inference for Categorical Data: Chi-Square

📈Unit 9: Inference for Quantitative Data: Slopes

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