Question: Determine whether the points in each scatter plot have a positive correlation, a negative correlation, or no correlation.
Then, determine which r-value is most accurate.
Sample Problem
r = 0.8
r = -0.8
r = 0.08
r = -0.08
The data show a positive correlation because as the x-values increase, the y-values increase. When a line of best fit is drawn, the data points are closely bunched to the line. As a result, the value of r will be positive and close to 1. From the choices, the most accurate response is r = 0.8.
Graph at top-left: a scatter plot with points trending upward from left to right, showing positive correlation.
Select all the correct answers.
positive correlation
negative correlation
no correlation
r = 0.9
r = -0.6
r = 0.02
r = -0.006
Graph at top-right: a scatter plot with points trending downward from left to right, showing negative correlation.
1. **State the problem:** We need to determine the type of correlation (positive, negative, or none) for two scatter plots and identify the most accurate correlation coefficient $r$ from the given options.
2. **Recall correlation basics:**
- Positive correlation means as $x$ increases, $y$ also increases.
- Negative correlation means as $x$ increases, $y$ decreases.
- No correlation means no clear pattern between $x$ and $y$.
- The correlation coefficient $r$ ranges from $-1$ to $1$, where values close to $\pm 1$ indicate strong correlation and values near $0$ indicate weak or no correlation.
3. **Analyze the top-left graph:** Points trend upward from left to right, indicating a positive correlation.
4. **Choose the most accurate $r$ for top-left:** Among $r=0.9$, $r=-0.6$, $r=0.02$, and $r=-0.006$, the positive and close to 1 value is $r=0.9$.
5. **Analyze the top-right graph:** Points trend downward from left to right, indicating a negative correlation.
6. **Choose the most accurate $r$ for top-right:** Among the same $r$ values, the negative value closest to $-1$ is $r=-0.6$.
**Final answers:**
- Top-left graph: positive correlation, $r=0.9$
- Top-right graph: negative correlation, $r=-0.6$