Question

A study was conducted to examine the quality of fish after seven days in ice storage. For this study Y = measurement of fish quality (on a 10-point scale with 10 = BEST.)

X = # of hours after being caught that the fish were packed in ice. The sample linear regression line is: Y = 8.5 - .5X. From this we can say that:

a. a one-hour delay in packing the fish in ice increases the estimated quality by 0.5.
b. Can't really say until we see a plot of the data.
c. a one-hour delay in packing the fish in ice decreases the estimated quality by 0.5.
d. if the estimated quality increases by 1, then the fish have been packed in ice two hours later.
e. if the estimated quality increases by 1, then the fish have been packed in ice one hour sooner.

Answer 1

From this we can say that;

c. A one-hour delay in packaging the fish in ice decreases the estimated quality by 0.5

Explanation:

The sample linear regression line representing the study of the relationship between the quality of fish, 'Y', and the number of hours that elapse after being caught that the fish were packed in ice, 'X', is presented as follows;

Y = 8.5 - 0.5·x

The estimated quality of a fish after a 1 hour delay in packaging in ice, is given as follows;

When X = 1

Y = 8.5 - 0.5 × 1 = 8.0

Therefore, the quality of a fish decreases from 8.5 to 8.0 which is equivalent to a 0.5 decrease in the quality of the fish, after a 1 hour delay in packaging in ice after being caught.