https://file.aiquickdraw.com/mathbot/file/1727409210606zr5n5bg4.jpg

Let's start by finding the regression equation \( y = ax + b \) using the given data points.

The given data is:
\[
x = [11.5, 8.2, 6.6, 2.3, 2.2, 2.5, 0.7]
\]
\[
y = [14, 11.1, 9.6, 6.8, 6.1, 5.9, 4.6]
\]

First, we'll calculate the slope \( a \) and the intercept \( b \) using the least squares method. Then, we will use the regression equation to predict values for parts (A) and (B).

Let me calculate this.The regression equation in the form \( y = ax + b \) is:
\[
y = 0.85x + 4.19
\]
(rounded to two decimal places)

Now, using this equation:

**A) For a state with 8.8 thousand automatic weapons, the expected murder rate per 100,000 residents is:**
\[
y = 0.85(8.8) + 4.19 = 11.637
\]
Rounded to three decimal places: **11.637**

**B) For a state with 8.9 thousand automatic weapons, the expected murder rate per 100,000 residents is:**
\[
y = 0.85(8.9) + 4.19 = 11.721
\]
Rounded to three decimal places: **11.721**

Would you like more details or have any other questions?

### Here are 5 related questions:
1. How is the slope of the regression line interpreted in this context?
2. What does the intercept represent in real-world terms?
3. How would predictions change if there were an outlier in the data?
4. How would you evaluate the accuracy of this regression model?
5. How does correlation impact the reliability of the regression equation?

**Tip:** Regression analysis is powerful for predicting trends but always check the correlation coefficient to gauge the strength of the relationship.

Determine the regression equation in y = ax + b form using the given data of thousands of automatic weapons and the murder rates for several Northwestern states. Then, predict the murder rates for states with 8.8 and 8.9 thousand automatic weapons.

Learn how to apply linear regression to predict murder rates based on the number of automatic weapons using a dataset from Northwestern states. This tutorial includes steps to calculate the regression equation and predict values for specific scenarios.

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