IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
A scatterplot of monthly premium income (x, in ₹ lakh) against claims (y, in ₹ lakh) for a Mumbai insurer gives r = 0.80. Every x value is then converted to ₹ crore (divided by 100) and every y value is increased by 5. What is the new correlation coefficient?
The correlation stays at 0.80. Correlation is invariant to location shifts and positive rescaling of either variable, so converting lakh to crore and adding a constant leaves it unchanged.
- A0.008
- B0.85
- C0.80Correct
- D0.40
- -0.80
Explanation
Correlation is unchanged by positive linear transformations of either variable, that is by changes of origin and positive scale. Both transformations here are of that kind, so r remains 0.80. Dividing r by 100 would wrongly treat it as scale dependent.
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