Find the equation of the regression line for an association that's positive and weak, with the correlation coefficient, r, being 0.14

To find the equation of the regression line, we generally follow the form:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the regression line,
- \(b\) is the y-intercept.

Since you've indicated that the correlation coefficient \(r = 0.14\), this tells us the strength and direction of the relationship between the variables, but we need more information to compute the full equation, such as the means, standard deviations, and covariance of the variables involved. Here's the general procedure to determine the equation:

1. **Find the slope (\(m\))** using the formula:
   \[
   m = r \cdot \frac{s_y}{s_x}
   \]
   where:
   - \(r\) is the correlation coefficient,
   - \(s_y\) is the standard deviation of the \(y\)-values,
   - \(s_x\) is the standard deviation of the \(x\)-values.

2. **Find the intercept (\(b\))** using the formula:
   \[
   b = \bar{y} - m \cdot \bar{x}
   \]
   where:
   - \(\bar{y}\) is the mean of the \(y\)-values,
   - \(\bar{x}\) is the mean of the \(x\)-values,
   - \(m\) is the slope you calculated.

Without more specific details such as means or standard deviations, I can only explain the method rather than give the exact equation. If you provide those, I can calculate the equation of the regression line directly.

Do you have any additional information, or would you like further details?

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### Related Questions:
1. How do we compute standard deviations if only raw data is given?
2. What is the impact of a weak correlation (such as \(r = 0.14\)) on predictions made by the regression line?
3. How does the sign of \(r\) affect the direction of the slope?
4. What assumptions do we make in linear regression?
5. How does outlier presence influence the correlation coefficient and regression line?

### Tip:
A weak correlation (like \(r = 0.14\)) means the regression line will not fit the data points very closely, so predictions based on this line could be less accurate.

Learn how to determine the equation of a regression line when the correlation is weak and positive (r = 0.14). This guide explains key statistical concepts, including the use of formulas for slope and intercept in linear regression. Suitable for students in Grades 10-12.

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