Question

1. How do we decide if the correlation coefficient is close enough to ±±1 to declare that there is correlation? [2 sentences]
2. How can you find the correct value of the correlation coefficient from the coefficient of determination? [2 sentences]
3. What is the problem with using a regression equation to predict what will happen in the distant future? Provide a specific example and show how this could cause problems. [3 sentences]

Answer 1

SOLUTION

1 ANS) Sometimes correlation is enough. For example, in car insurance, male drivers are correlated with more accidents, so insurance companies charge them more. There is no way you could actually test this for causation. You cannot change the genders of the drivers experimentally. Google has made hundreds of billions of dollars not caring about causation.

2 ANS)

IN statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1. To interpret its value, see which of the following values your correlation r is closest to:

• Exactly –1. A perfect downhill (negative) linear relationship

• –0.70. A strong downhill (negative) linear relationship

• –0.50. A moderate downhill (negative) relationship

• –0.30. A weak downhill (negative) linear relationship

• 0. No linear relationship

• +0.30. A weak uphill (positive) linear relationship

• +0.50. A moderate uphill (positive) relationship

• +0.70. A strong uphill (positive) linear relationship

• Exactly +1. A perfect uphill (positive) linear relationship

3 ans) Many folks make the mistake of thinking that a correlation of –1 is a bad thing, indicating no relationship. Just the opposite is true! A correlation of –1 means the data are lined up in a perfect straight line, the strongest negative linear relationship you can get. The “–” (minus) sign just happens to indicate a negative relationship, a downhill line.

How close is close enough to –1 or +1 to indicate a strong enough linear relationship? Most statisticians like to see correlations beyond at least +0.5 or –0.5 before getting too excited about them. Don’t expect a correlation to always be 0.99 however; remember, these are real data, and real data aren’t perfect.