The correlation coefficient computed from a set of 30 observation is 0.8. Then the percentage of variation not explained by linear regression is

Options

A. `80%`
B. `20%`
C. `64%`
D. `36%`

Answer

To solve the problem, we need to determine the percentage of variation not explained by linear regression given the correlation coefficient.

### Step-by-Step Solution:

1. **Identify the Correlation Coefficient (r)**:
The correlation coefficient given in the problem is \( r = 0.8 \).

2. **Calculate the Coefficient of Determination (r²)**:
The coefficient of determination is calculated by squaring the correlation coefficient:
\[ r^2 = (0.8)^2 = 0.64 \]

3. **Convert r² to Percentage**:
To express the coefficient of determination as a percentage, we multiply it by 100:
\[ \text{Percentage of variation explained} = r^2 \times 100 = 0.64 \times 100 = 64\% \]

4. **Calculate the Percentage of Variation Not Explained**:
The percentage of variation not explained by the linear regression is found by subtracting the percentage of variation explained from 100%:
\[ \text{Percentage of variation not explained} = 100\% - 64\% = 36\% \]

5. **Final Answer**:
Therefore, the percentage of variation not explained by linear regression is \( \boxed{36\%} \).