# Exciting Data Analysis Fun!

## Are you ready to dive into the world of data analysis?

Let's start by analyzing the following data:

- Sample slope: 5.43
- Sample intercept: 10.2
- x1: 22
- y1: 140

What is the residual for the first observation?

## The Exciting Answer!

The residual for the first observation is 7.23. Want to know how we calculated it? Let's dig deeper into the details!

## Exciting Data Analysis Adventure!

Let's break down how we arrived at the residual for the first observation. In this case, we have a regression line defined by the sample slope of 5.43 and intercept of 10.2, with x1 as 22 and y1 as 140.

To calculate the residual, we first need to find the predicted y value (y_hat) using the regression line equation:

**y_hat = slope * x + intercept**

By plugging in the values, we get:

**y_hat = 5.43 * 22 + 10.2 = 125.46**

The residual is then determined by finding the difference between the observed y value and the predicted y value:

**residual = y1 - y_hat = 140 - 125.46 = 7.23**

This means that the actual observed value is 7.23 units higher than what the regression line would predict. Isn't data analysis exciting?