In which one of the following cases would you expect to get a negative correlation?
Insurance companies’ profits and the number at claims they have to pay
Understanding Negative Correlation
Correlation is a statistical measure that describes the extent to which two variables change together. It indicates both the direction and strength of the relationship between the variables. A correlation can be positive, negative, or zero.
- Positive Correlation: When two variables tend to increase or decrease together. As one variable goes up, the other generally goes up as well.
- Negative Correlation: When two variables tend to move in opposite directions. As one variable goes up, the other generally goes down.
- Zero Correlation: When there is no consistent relationship between the two variables.
Analyzing Potential Scenarios for Negative Correlation
Let's examine each given scenario to determine which one is most likely to exhibit a negative correlation.
- The ages of husbands and wives: In most marriages, the ages of husbands and wives are quite similar. If the husband's age increases, the wife's age is also likely to increase (or be close to his age). This relationship typically shows a positive correlation.
- Shoe size and intelligence: There is generally no known relationship between a person's shoe size and their intelligence level. These two variables are independent of each other. We would expect to see little to zero correlation.
- Insurance companies’ profits and the number of claims they have to pay: An insurance company makes profits from premiums paid by policyholders. When the number of claims the company has to pay increases, their expenses rise significantly. Higher expenses directly reduce the company's net profit, assuming revenues (premiums) remain constant. Therefore, as the number of claims increases, profits tend to decrease. This is a classic example of a negative correlation.
- Amount of rainfall and yield of crop: For many crops, a certain amount of rainfall is essential for growth. Up to an optimal point, more rainfall generally leads to a higher crop yield (positive correlation). However, excessive rainfall can damage crops and reduce yield (negative correlation beyond the optimum). But overall, in many typical agricultural contexts, the relationship is often positive or curvilinear rather than consistently negative across the entire range. Compared to the insurance example, a negative correlation is less consistently expected here.
Expected Correlation Summary Table
| Scenario | Expected Correlation | Reasoning |
|---|---|---|
| Ages of husbands and wives | Positive | Ages tend to be similar; as one increases, the other is likely to be higher too. |
| Shoe size and intelligence | Zero | No meaningful relationship exists. |
| Insurance company profits and claims paid | Negative | More claims mean higher expenses, leading to lower profits. |
| Amount of rainfall and crop yield | Often Positive (up to a point) | Rainfall helps crops grow, but too much can be harmful. Negative correlation is possible but less consistent than in the insurance example. |
Based on the analysis, the scenario involving insurance companies' profits and the number of claims they have to pay is the one where you would most strongly expect to get a negative correlation.
Revision Table: Correlation Basics
| Type of Correlation | Description | Example |
|---|---|---|
| Positive | Variables move in the same direction ($\uparrow \uparrow$ or $\downarrow \downarrow$) | Hours studied and exam scores |
| Negative | Variables move in opposite directions ($\uparrow \downarrow$ or $\downarrow \uparrow$) | Price of a product and quantity demanded |
| Zero | No consistent linear relationship | Height and happiness level |
Additional Information: Correlation vs. Causation
It's important to remember that correlation does not imply causation. Just because two variables are correlated (positively or negatively) does not mean that one variable causes the other to change. There might be other factors influencing both variables, or the observed correlation could be coincidental.
For example, while there is a negative correlation between insurance profits and claims, paying claims is a direct expense that contributes to lower profits, suggesting a causal link. However, in other situations, a third variable could be responsible for the observed correlation. Always be careful about making conclusions about cause and effect based solely on correlation.
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Important Questions from Correlation and Regression
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Statement ll: The variance of the error, or disturbance, term is not the same regardless of the value of the explanatory variable under OLS.
In light of the above statements, choose the most appropriate answer from the options given below
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Which of the following statements relating to Correlation and Regression are true?
(a) The Coefficient of Correlation is independent of change of origin and scale.
(b) The Coefficient of Correlation between the two variables is the arithmetic average of the two Regression Coefficients.
(c) The probable error of the Coefficient Correlation is 0.6745 times its standard error.
(d) Coefficient of Correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line.
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If two regression coefficients are 0.8 and 1.2, which one of the following is the value of coefficient of correlation?
