If the two regression coefficient are negative then value of correlation coefficient will be positive
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To get this effect, there has to be positive correlation between the two predictors involved, as you have.
Here's an example from my own experience (insurance risk). The claim rate for motor insurance is positively correlated with year of manufacture: more recently-built cars have more claims. It's also positively correlated with sum insured: more expensive cars have more claims. However, when you include both predictors, you find that claim rate has a negative relationship with year of manufacture: for a given value, more recently-built cars have fewer claims than earlier ones. This is because for a given value, an older car is likely to be an inherently more prestigious/higher-status make or model which has suffered the effects of depreciation. On the other hand, a newer vehicle insured for the same amount is likely to be a more mass-market brand. Pricier, more valuable brands are more likely to claim, and this is brought out when both effects (vehicle age and sum insured) are included in the analysis
Here's an example from my own experience (insurance risk). The claim rate for motor insurance is positively correlated with year of manufacture: more recently-built cars have more claims. It's also positively correlated with sum insured: more expensive cars have more claims. However, when you include both predictors, you find that claim rate has a negative relationship with year of manufacture: for a given value, more recently-built cars have fewer claims than earlier ones. This is because for a given value, an older car is likely to be an inherently more prestigious/higher-status make or model which has suffered the effects of depreciation. On the other hand, a newer vehicle insured for the same amount is likely to be a more mass-market brand. Pricier, more valuable brands are more likely to claim, and this is brought out when both effects (vehicle age and sum insured) are included in the analysis
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Answer:
The values cannot exceed 1.0 or be less than -1.0, and a correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation. Anytime the correlation coefficient is greater than zero, it's a positive relationship.
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