In a study conducted to examine the quality of fish after 7 days in ice storage,
ID: 3258371 • Letter: I
Question
In a study conducted to examine the quality of fish after 7 days in ice storage, ten raw fish of the same kind and approximately the same size were caught and prepared for ice storage. The fish were placed in ice storage at different times after being caught. A measure of fish quality was given to each fish after 7 days in ice storage. Review the accompanying sample data, scatterplot, and Minitab output from a simple linear regression analysis, where "Time" is the number of hours after being caught that the fish was placed in ice storage and "Fish Quality" is the measure given to each fish after 7 days in ice storage (higher numbers mean better quality). What percentage of the variation in "Fish Quality" is accounted by this linear regression model with "Time" as the explanatory variable?
Choose the correct answer below.
A.
99.0%
B.
98.1%
C.
0.990%
D.
9.50%
E.
0.150%
Table is below
Time
0
0
2
3
5
6
7
9
11
12
Fish Quality
8.5
8.4
8.0
8.1
7.8
7.6
7.3
7.0
6.8
6.7
048126789Time (hours)Fish Quality
Edit Coordinates... (0,0)
A scatterplot has a horizontal axis labeled Time in hours from negative 2 to 14 in increments of 2 and a vertical axis labeled Fish Quality from 6 to 9 in increments of 0.5. The scatterplot contains ten plotted points that closely follow a pattern of falling from left to right at a constant rate from (0, 8.5) to (12, 6.7), with all points falling within 0.3 vertical units of this pattern. All coordinates are approximate.
Minitab Output
Predictor Coef StDev T P
Constant 8.44252 0.05043 167.43 0.000
Time -0.149550 0.007363 -20.31 0.000
S = 0.09501 R-Sq = 98.1% R-Sq(adj) = 97.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 3.7238 3.7238 412.51 0.000
Residual Error 8 0.0722 0.0090
Total 9 3.7960
Time
0
0
2
3
5
6
7
9
11
12
Fish Quality
8.5
8.4
8.0
8.1
7.8
7.6
7.3
7.0
6.8
6.7
Explanation / Answer
percentage of the variation in "Fish Quality" is accounted by this linear regression model with "Time" as the explanatory variable is given by R^2
here R-sq = 98.1 % (see the table )
B) R^2 = 98.1% is correct