cdude
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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.


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


Answer

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.
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Nishantkumar19
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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.
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Gregorius
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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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