Alright, let’s go step by step to connect the **t-value (0.672)** to the **Pearson correlation coefficient (r)**.
---
## ✅ Step 1: Use the formula connecting *t* and *r*
The relationship is:
[
t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}
]
Where:
* ( t ) = 0.672 (given)
* ( n ) = number of data points
* ( r ) = correlation coefficient (what we want)
---
## ✅ Step 2: Get the sample size (n)
From your scatter plot, there are about **15 data points** (you can count them).
So:
[
n = 15
]
---
## ✅ Step 3: Substitute values
[
0.672 = \frac{r\sqrt{15-2}}{\sqrt{1-r^2}}
]
[
0.672 = \frac{r\sqrt{13}}{\sqrt{1-r^2}}
]
---
## ✅ Step 4: Simplify
[
\sqrt{13} \approx 3.606
]
So:
[
0.672 = \frac{3.606r}{\sqrt{1-r^2}}
]
---
## ✅ Step 5: Multiply both sides
[
0.672 \sqrt{1-r^2} = 3.606r
]
---
## ✅ Step 6: Square both sides
[
(0.672)^2 (1 - r^2) = (3.606r)^2
]
[
0.451 (1 - r^2) = 13.01 r^2
]
---
## ✅ Step 7: Expand
[
0.451 - 0.451r^2 = 13.01r^2
]
---
## ✅ Step 8: Combine like terms
[
0.451 = 13.461r^2
]
---
## ✅ Step 9: Solve for r
[
r^2 = \frac{0.451}{13.461} \approx 0.0335
]
[
r = \sqrt{0.0335} \approx 0.183
]
---
## ✅ Final Answer
### **r ≈ +0.18**
---
## ✅ Interpretation (for #6)
* **Direction:** Positive
* **Strength:** Weak
* **Conclusion:** Very slight relationship, not significant
---
If you want, I can also show a **shortcut method using a calculator or Excel** (much faster for exams).
input this in excel
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