Question

Will give 100 points;

In the U.S., from 2004-2015, the correlation coefficient for the relationship between the size of a cell phone data plan, x, and the number of text messages sent, y, is r =0.97. Describe what this means about the relationship between the data plan size and the number of text messages sent in the U.S.

Answer options:
- There is no correlation between the size of the data plan and the number of text messages in the US.
- There is a weak positive linear correlation between the size of a cell phone data plan and the number of text messages sent.
- There is a strong negative linear correlation between the size of a cell phone data plan and the number of text messages sent.
- There is a strong positive linear correlation between the size of a cell phone data plan and the number of text messages sent.

I'd appreciate if you included an explanation, but an answer is fine.

Answer 1

- There is a strong positive linear correlation between the size of a cell phone data plan and the number of text messages sent is your answer

Answer 2

• D. There is a strong positive linear correlation between the size of a cell phone data plan and the number of text messages sent.

Explanation:

We have r = 0.97

• Correlation coefficients whose magnitude are between 0.9 and 1.0 indicate variables which can be considered very highly correlated (as per below table)

• r = (0.9, 1.0) very highly correlated.
• r = (0.7, 0.9) highly correlated.
• r = (0.5, 0.7) moderately correlated.
• r = (0.3, 0.5) low correlation.
• r = (0, 0.3) little to no correlation.

Same applies to negative side

Correct choice is

• D. There is a strong positive linear correlation between the size of a cell phone data plan and the number of text messages sent.

To explain it in very simple way, consider a linear equation:

• y = mx + b

Number of text messages is the linear function of the data plan. r = 0.97 shows this relationship is almost a perfect line with positive slope.