# Correlation Coefficient

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#1
I'm unsure about how they came up with 'Correlation coefficient: 0.9886'

How do i work out the correlation coefficient from the data provided?

A food company wanted to know if the amount of taste enhancer added to one of its products has any effect. It ran a test by adding eight different amounts and asking a panel of tasters to rank the results.

Table 2 Food company data

(See attachment)

See below the corresponding Excel regression output.

Question
1. a. Comment on the relationship between the amount of enhancer and the ranking by the panel. Clearly justify your claim.

Correlation coefficient: 0.9886

Strong positive correlation between amount of enhancers and the rank by the panel.

A large number of enhancers added to the food seems to be associated with a higher rank of the food. Considering a scale from 1 to 10, with 1 representing a ‘low‘ rank and 10 a ‘high’ rank.
0
4 years ago
#2
If you square root the value they give for Multiple R (0.977359), you get 0.9886, which is the correlation coefficient in the answer.

I'm not sure if that's how it actually works. I just sorta stumbled upon that.
0
4 years ago
#3
This is all distinctly odd. The value given is the square root of the pearson correlation coefficient. However, one of the vectors is a set of ranks, so a rank correlation coefficient would make much more sense!

Similarly, linear regression is not an appropriate means of analysis as the outcome variable is a rank.
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