Correct option is D
Given Information from the Graph:
- Regression equation:
Profit = 4T - 86 - Correlation coefficient:
r = 0.83
Option A:
Statement: "The sum of the squared differences between the observed and estimated values of profit is minimum."
This is CORRECT.
Explanation: This is the fundamental principle of the least squares method. It always minimizes the sum of the squared differences between the actual observed values and the predicted values from the regression line.
Option B:
Statement: "About 69% of the variation in profit is explained by the variation in temperature."
This is CORRECT.
Explanation: The coefficient of determination is r².
So, r = 0.83 → r² = 0.83 × 0.83 = 0.6889 ≈ 69%.
This means about 69% of the variation in profit is explained by temperature.
Option C:
Statement: "At 30°C, estimated profit is 34 million Rs."
This is CORRECT.
Check using the regression equation:
Profit = 4 × 30 - 86 = 120 - 86 = 34 million Rs.
Option D:
Statement: "Data point (32, 80) is anomalous and therefore must be discarded."
This is INCORRECT.
Explanation:
Although the point (32, 80) appears to deviate from the line, it should not be immediately discarded. Outliers need proper statistical justification before removal.
Also, the correlation coefficient (r = 0.83) indicates a strong positive relationship, so the data is still reliable overall.
Final Answer: (D) is the incorrect statement.
