There is a strong positive linear correlation between the number of rainy days and the number of tomatoes produced on a tomato plant. Does this mean
that more rainy days cause the tomato plants to produce more?
A. No. Any number of factors could also affect the number of
tomatoes produced.
B. Yes. Since the number of rainy days and number of tomatoes
produced are linearly correlated, this means a greater number of
rainy days causes the tomato plants to produce more.
C. No. Since the number of rainy days and number of tomatoes
produced are linearly correlated, this means a smaller number of
rainy days causes the tomato plants to produce more.
D. Yes. Since the number of rainy days and number of tomatoes
produced are positively correlated, this means a greater number of
rainy days causes the tomato plants to produce more.

The correct answer is D. Yes. Since the number of rainy days and number of tomatoes produced are positively correlated, this means a greater number of rainy days cause the tomato plants to produce more.

Explanation:

A positive correlation implies two variables or factors increase or decrease together. This is the opposite of a negative correlation as, in this, variables move in opposite directions. In this context, if the number of tomatoes and the number of rainy days have a positive correlation more rainy days imply more tomatoes and vice versa.

According to this, option D is correct as an increase in the rainy days leads to an increase in the production of tomatoes. Moreover, this is caused by the positive correlation, while the linear correlation only means in a graph the two variables will form a line, but this does not indicate the variables increase together.

The power of the root of the power of a variable can be written as a rational power by creating a rational exponent that is the product of the powers divided by the root. The rational exponent should be reduced to lowest terms. For example, the seventh power of the sixth root of the fifth power of x will be x^(7*5/6) = x^(35/6).
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