Statistics - Correlation Coefficient/Regression
posted by Hannah on .
'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:
I'm having trouble getting the correlation coefficient. I used the formula in my textbook:
r=nΣxy-(Σx)( Σy) / √n(Σx²)-(Σx)² * √n(Σy²)-(Σy)²
but I keep coming up with different answers (I've done it by hand & with my TI-84 plus (LinRegTTest) several times each). I've figured out b1 (14.42378282) for the slope equation but for b0, my answer keeps changing (I get -15.something & the "something" is what keeps changing every time I work the problem out).
I used an online calculator and came up with this:
y = a + bx where:
r = 0.978
Your formula looks correct. It's easy to make errors with the calculations when doing these kinds of problems.
y = -15.4 + 14.4x
the correlation coefficient is correct because it is geomatric mean of two regression coefficient the second regression coefficient is 0.066428.