 A U.S. state's Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The following table gives the approximate number of jobs for the citizens that would be created at various levels of recovery.
Percent Recovery (%)	20	40	80	100
Jobs Created (Millions)	5	8	11	17
Find the regression line.

To find the regression line that best fits the data given, we need to model the relationship between the percent recovery (\( x \)) and the number of jobs created (\( y \)) using a linear equation:

\[
y = mx + b
\]

Where:
- \( y \) is the number of jobs created (in millions),
- \( x \) is the percent recovery,
- \( m \) is the slope of the regression line,
- \( b \) is the y-intercept.

The data points provided are:

\[
(20, 5), (40, 8), (80, 11), (100, 17)
\]

### Step 1: Calculate the means of \( x \) and \( y \)
- \( \bar{x} = \frac{20 + 40 + 80 + 100}{4} = 60 \)
- \( \bar{y} = \frac{5 + 8 + 11 + 17}{4} = 10.25 \)

### Step 2: Calculate the slope (\( m \))
The formula for the slope is:

\[
m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}
\]

### Step 3: Calculate the intercept (\( b \))
The y-intercept is given by:

\[
b = \bar{y} - m\bar{x}
\]

Let's calculate these values step by step.The regression line that models the relationship between the percent recovery (\( x \)) and the number of jobs created (\( y \)) is:

\[
y = 0.135x + 2.15
\]

This equation means that for every 1% increase in recovery, approximately 0.135 million jobs are created, starting with an initial estimate of 2.15 million jobs.

Do you have any questions or need further details?

Here are some related questions:
1. How can this regression line be used to predict the number of jobs at a different percent recovery?
2. What are the limitations of using a linear regression model in this context?
3. Can we estimate the recovery percentage that would lead to zero job creation?
4. How could adding more data points improve the accuracy of the model?
5. How would the regression change if the job numbers increased exponentially?

**Tip:** Always check if the data follows a linear trend before applying a linear regression model.

A U.S. state's Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The following table gives the approximate number of jobs for the citizens that would be created at various levels of recovery. Percent Recovery (%) 20 40 80 100 Jobs Created (Millions) 5 8 11 17 Find the regression line.

Discover how to find the linear regression line for the relationship between percent recovery of oil using CO2 EOR technology and the number of jobs created. This guide includes detailed steps, including the formula y = 0.135x + 2.15, which predicts job creation based on recovery percentages. Suitable for high school students in Grades 9-12.

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