A market manager of a large supermarket chain used shelf space for pet food to p
ID: 3359955 • Letter: A
Question
A market manager of a large supermarket chain used shelf space for pet food to predict weekly sales. The manager collected data on shelf space and weekly sales from a random sample of 12 equal-sized stores. For those data, SSR=19,915 and SST=29,546. Use this information to complete parts (a) through (c) below.
Determine the coefficient of determination, r2, and interpret its meaning.
r2=___ (Round to three decimal places as needed.)
Interpret the meaning of r2.
It means that ___% of the variation in
shelf space
pet food sales
can be explained by the variation in
pet food sales.
shelf space.
(Round to one decimal place as needed.)
b. Determine the standard error of the estimate.
SYX=____(Round to four decimal places as needed.)
c. How useful do you think this regression model is for predicting weekly pet food sales?
A.
It is very useful for predicting weekly pet food sales because the coefficient of determination is close to 1.
B.
It is not very useful for predicting weekly pet food sales because the coefficient of determination is close to 1.
C.
It is not very useful for predicting weekly pet food sales because the coefficient of determination is close to 0.
D.
It is very useful for predicting weekly pet food sales because the coefficient of determination is close to 0.
Explanation / Answer
we know that
r2 can be calculated as
SSR/SST
= 19915/29546 = 0.674
This means that 67.4% variation in weekly sales can be explained by variation on shelf space
b
we know that
SSR + SSerror = SS Total
so SSerror = 29546-19915 = 9631
c)
higher the r2 values better the model , here the value is 0.674 , so we can say that It is very useful for predicting weekly pet food sales because the coefficient of determination is close to 1.
Hence A
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