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
y
10
9
8
7
6
5
4
3
2
1
0
x
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.
y
10
9
8
7
6
5
4
3
2
1
0
x
Select all the correct answers.
positive correlation
negative correlation
no correlation
r = 0.01
r = 0.8
r = 0.5
r = 0.5
Graph shape and math position_hint:
top-left: scatter plot shows a positive correlation with points rising from lower left to upper right, matching the sample problem0s upward trend and suggesting r = 0.8.
top-right: scatter plot shows no clear correlation; points are scattered without a consistent upward or downward trend, so r is closest to 0.01.
1. **State the problem:**
We need to determine the type of correlation (positive, negative, or none) for each scatter plot 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 $1$.
- $r$ close to $1$ means strong positive correlation.
- $r$ close to $-1$ means strong negative correlation.
- $r$ close to $0$ means no correlation.
3. **Analyze the sample problem:**
- The points rise from lower left to upper right.
- This indicates a positive correlation.
- The points are close to the line of best fit.
- So, $r$ should be positive and close to $1$.
- Among the options $r=0.8$, $r=-0.8$, $r=0.08$, $r=-0.08$, the best choice is $r=0.8$.
4. **Analyze the new scatter plots:**
- **Top-left plot:** Points rise from lower left to upper right.
- This shows a positive correlation.
- Among $r=0.01$, $r=0.8$, $r=-0.5$, $r=0.5$, the closest positive and strong correlation is $r=0.8$.
- **Top-right plot:** Points are scattered randomly without a clear trend.
- This indicates no correlation.
- Among the $r$ values, $r=0.01$ is closest to zero, indicating no correlation.
5. **Final answers:**
- Top-left plot: positive correlation, $r=0.8$.
- Top-right plot: no correlation, $r=0.01$.