What is the coefficient of correlation between sales and price?

In summary, the conversation discusses a sample of 21 observations that found an inverse relationship between sales and price, with a coefficient of determination that is 106% of the adjusted coefficient of determination. It also mentions the variance of sales around the mean being 640 and asks about the coefficient of correlation. The coefficient of determination is equivalent to the variance and is calculated using the formula SSR/SST. The conversation also mentions the definition of coefficient of correlation as the covariance between two variables divided by their standard deviations.
  • #1
adeel
45
0
In a sample of 21 observations obtained it was found that sales and price have an inverse relationship and coefficient of determination is 106% as much as the adjusted coefficient of determination. It is also known that the variance of sales around mean is 640. What is the coefficient of correlation?

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Im not sure how all the information fits together. I know coefficient of determination is SSR/SST, but i don't have any of that information
 
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  • #2
im not really sure what variance of sales around mean, means...help?
 
  • #3
is sum of squares total the same as the variance around the mean?
 
  • #4
adeel said:
is sum of squares total the same as the variance around the mean?

Variance is the coefficient of determination, which is the square of the coefficient of correlation. Adjusted, I think, means calculated from a linear regression with outliers eliminated. However, I may be totally wrong :redface:. In any case, http://encyclopedia.thefreedictionary.com/Coefficient+of+determination might help.
 
  • #5
Another way coef of corr between X and Y is defined is Corr(X,Y) = Cov(X,Y)/([itex]\sigma_X\sigma_Y[/itex]) where "sigma" is the standard dev. of the subscripted variable. Maybe it is this formula that the problem is asking about?
 

What is the coefficient of correlation?

The coefficient of correlation, also known as Pearson's correlation coefficient, is a statistical measure that describes the strength and direction of the linear relationship between two continuous variables.

How is the coefficient of correlation calculated?

The coefficient of correlation is calculated by dividing the covariance of two variables by the product of their standard deviations. This results in a value between -1 and 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

What does a high or low coefficient of correlation indicate?

A high coefficient of correlation (close to 1 or -1) indicates a strong linear relationship between the two variables, meaning that as one variable increases, the other tends to also increase or decrease in a predictable manner. A low coefficient of correlation (close to 0) indicates little to no linear relationship between the two variables.

Can the coefficient of correlation be used to determine causation?

No, the coefficient of correlation only measures the strength and direction of a linear relationship between two variables. It does not indicate causation, as there could be other factors at play that influence the relationship between the variables.

What are some limitations of the coefficient of correlation?

The coefficient of correlation only measures the strength and direction of a linear relationship, and may not accurately represent the relationship between variables if there is a nonlinear relationship. Additionally, it is sensitive to outliers and can be affected by the range and variability of the data.

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