Thread: Correlation Coefficent & Regression Equation

I'm having some difficulty with the following question:


The following data shows expenditures (in millions of dollars) and case (sales in millions) for 7 major soft drink brands. Calculate the correlation coefficient. Is this significant at the 5% level (ie, α=.05)? Construct the regression equation for this data. Decide how much RC Cola would make if they spend 643.8. Do the same for Canada Dry if they spend 13.8. Is it a good idea to use this regression equation for RC and Canada Dry? Why?

Brand Spending Sales
Coke 131.3 1929.2
Pepsi 92.4 1384.6
Diet Coke 60.4 811.4
Sprite 55.7 541.5
Dr Pepper 40.2 536.9
Mt Dew 29.0 535.6
7-Up 11.6 219.5
I made my table & came up with:
Ex=420.6
Ey=5958.7
Exy=500073.09
Exsq=35119.7
Eysq=7213830.96

However, when I used the r formula by hand & by calculator, I came up with 2 different answers: -275.4830985 (hand) & 0.9721001417 (TI-84 calculator). If the calculator is right, how do I get to that answer?

Also, any other help anyone can give me with the rest of the problem would be appreciated!

Thanks!

Originally Posted by ridley1013

I'm having some difficulty with the following question:


The following data shows expenditures (in millions of dollars) and case (sales in millions) for 7 major soft drink brands. Calculate the correlation coefficient. Is this significant at the 5% level (ie, α=.05)? Construct the regression equation for this data. Decide how much RC Cola would make if they spend 643.8. Do the same for Canada Dry if they spend 13.8. Is it a good idea to use this regression equation for RC and Canada Dry? Why?

Brand Spending Sales
Coke 131.3 1929.2
Pepsi 92.4 1384.6
Diet Coke 60.4 811.4
Sprite 55.7 541.5
Dr Pepper 40.2 536.9
Mt Dew 29.0 535.6
7-Up 11.6 219.5
I made my table & came up with:
Ex=420.6
Ey=5958.7
Exy=500073.09
Exsq=35119.7
Eysq=7213830.96

However, when I used the r formula by hand & by calculator, I came up with 2 different answers: -275.4830985 (hand) & 0.9721001417 (TI-84 calculator). If the calculator is right, how do I get to that answer?

Also, any other help anyone can give me with the rest of the problem would be appreciated!

Thanks!

Look up the required formula for the correlation coefficient and apply it.
(your expectations in the table you give are wrong first because they ought to be means and so of the same order as the data, second because if you are trying to use the expectations you have the wrong formula you need the sample correlation coefficient - see attachment which is the from the Wikipedia article on correlation coefficients).

RonL