Regression analysis

Blakeeie

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what procedures should i take, in order to verify whether a statement is true in regression analysis. E.g. there is a relationship between ice-cream sales figure (y) and ice-cream volume sold (x) (assumed that the relationship is not perfect maybe with a r=0.8), if someone said that the ice-cream sales figure will be approximately 20% of the ice-cream volume sold. what should i do to test whether the statement is true?
Confidence interval?


Thanks
 
what procedures should i take, in order to verify whether a statement is true in regression analysis. E.g. there is a relationship between ice-cream sales figure (y) and ice-cream volume sold (x) (assumed that the relationship is not perfect maybe with a r=0.8), if someone said that the ice-cream sales figure will be approximately 20% of the ice-cream volume sold. what should i do to test whether the statement is true?
Confidence interval?


Thanks
What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting


You might want to read something like
http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP
if you are talking about linear regression or possibly look at some of the other pages at
https://search.yahoo.com/yhs/search...nterval&ei=UTF-8&hspart=mozilla&hsimp=yhs-001
 
What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting


You might want to read something like
http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP
if you are talking about linear regression or possibly look at some of the other pages at
https://search.yahoo.com/yhs/search...nterval&ei=UTF-8&hspart=mozilla&hsimp=yhs-001

Well i have been thinking about the question for the whole day, and i am not sure whether i should use confidence interval estimate, prediction interval estimate, or do i simply look at the regression line.

Hence, i need to consult your expertise

thanks
 
Well i have been thinking about the question for the whole day, and i am not sure whether i should use confidence interval estimate, prediction interval estimate, or do i simply look at the regression line.

Hence, i need to consult your expertise

thanks
A statement that 'the ice-cream sales figure will be approximately 20% of the ice-cream volume sold' translates to
S ~ 0.2 V
where S is sales figure and V is volume sold. So, what does your fit look like? If it were
\(\displaystyle \overset{\wedge}{S}\, =\, 0.21\, V +0.01\)
and V was always large compared to .01/.21, say greater than 1, then yes S ~ 0.2 V would be a good estimate. If it were a different function which might appear not to indicate that at all, then depending on just what is wanted you should
(1) compute some kind of confidence interval for your fit if what you want is an estimation for present data
or
(2) compute some kind of prediction interval estimate if what you want is an estimation for future data. Note that this will probably involve computing some sort of 'goodness of fit' values such as an R2, Std. Est., confidence interval, etc. You will also need to obtain/assume a model for the 'errors' associated with the data. That is the actual data would be something like
yi = a + b xi + Ni
where the Ni are from some probability density function, i.e. possibly a normal distribution with mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\) which you would need to know or estimate.
 
A statement that 'the ice-cream sales figure will be approximately 20% of the ice-cream volume sold' translates to
S ~ 0.2 V
where S is sales figure and V is volume sold. So, what does your fit look like? If it were
\(\displaystyle \overset{\wedge}{S}\, =\, 0.21\, V +0.01\)
and V was always large compared to .01/.21, say greater than 1, then yes S ~ 0.2 V would be a good estimate. If it were a different function which might appear not to indicate that at all, then depending on just what is wanted you should
(1) compute some kind of confidence interval for your fit if what you want is an estimation for present data
or
(2) compute some kind of prediction interval estimate if what you want is an estimation for future data. Note that this will probably involve computing some sort of 'goodness of fit' values such as an R2, Std. Est., confidence interval, etc. You will also need to obtain/assume a model for the 'errors' associated with the data. That is the actual data would be something like
yi = a + b xi + Ni
where the Ni are from some probability density function, i.e. possibly a normal distribution with mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\) which you would need to know or estimate.

This is the regression analysis that i have computed on excel, so would i be able to say that the statement is true because 0.20, lies inbetween the 95% confidence interval? and do i just ignore the y-intercept?
attachment.php


Thanks,
Blake
 

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