# Lesson 4 Rocking the Residuals Solidify Understanding

### 1.

Interpret the data provided in the box plot for the first quiz of a unit of study for a group of math students.

What is the median score?

What is the range?

Did students do well on the quiz?

### 2.

Interpret the data provided in the box plot for the second quiz of a unit of study for a group of math students.

What is the median score?

What is the range?

Did students do well on the quiz?

### 3.

Look back at the box plots for problems 1 and 2. Which quiz did students perform better on the first quiz or the second quiz? Why?

Data is often collected using a survey with several questions. Questions that need to be answered with a number generate **numerical data**. Questions that produce responses that are not numbers generate **categorical data**.

Determine whether the questions in the following problems create **numerical data** or **categorical data**.

### 4.

What is your shoe size?

#### A.

numerical data

#### B.

categorical data

### 5.

What is the color of your eyes?

#### A.

numerical data

#### B.

categorical data

### 6.

What type of pet do you have?

#### A.

numerical data

#### B.

categorical data

### 7.

How tall are you?

#### A.

numerical data

#### B.

categorical data

### 8.

Where is your favorite place to visit?

#### A.

numerical data

#### B.

categorical data

### 9.

How many siblings do you have?

#### A.

numerical data

#### B.

categorical data

The data sets in problems 10 and 11 are scatterplots that have the regression line and the residuals marked. For each exercise, use the given data set to create a residual plot, and then assess the fit of the linear function to the data based on the residuals.

### 10.

Data Set 1

Residual Plot 1

### 11.

Data Set 2

Residual Plot 2

### 12.

Consider the residual plot below, determine whether the regression line is a good fit to the data or not, and then explain why it is or is not a good fit.

### 13.

Consider the residual plot below, determine whether the regression line is a good fit to the data or not, and then explain why it is or is not a good fit.

Decide if you agree or disagree with the following statements, and explain why.

### 14.

By analyzing the residuals, the quality of fit between a function and the data can be determined.

### 15.

When bivariate data have a strong correlation, that means that one of the data items causes the other item.

Find the solution and then interpret its meaning.