One measure of the viability of fish egges is percent dry mass(PctDM).
| Age |
PctDM |
Month |
Sept |
| 7 |
37.35 |
Nov |
0 |
| 8 |
38.05 |
Nov |
0 |
| 8 |
37.45 |
Nov |
0 |
| 9 |
38.95 |
Nov |
0 |
| 9 |
37.9 |
Nov |
0 |
| 9 |
36.45 |
Nov |
0 |
| 9 |
36.15 |
Nov |
0 |
| 10 |
38.35 |
Nov |
0 |
| 10 |
37.15 |
Nov |
0 |
| 11 |
36.5 |
Nov |
0 |
| 11 |
35.1 |
Nov |
0 |
| 12 |
37.7 |
Nov |
0 |
| 12 |
37.1 |
Nov |
0 |
| 13 |
37.4 |
Nov |
0 |
| 13 |
37.55 |
Nov |
0 |
| 13 |
36.35 |
Nov |
0 |
| 14 |
36.75 |
Nov |
0 |
| 15 |
37.05 |
Nov |
0 |
| 16 |
32.95 |
Nov |
0 |
| 17 |
36.15 |
Nov |
0 |
| 18 |
35.7 |
Nov |
0 |
| 7 |
34.9 |
Sep |
1 |
| 7 |
37 |
Sep |
1 |
| 7 |
37.9 |
Sep |
1 |
| 7 |
38.15 |
Sep |
1 |
| 9 |
33.9 |
Sep |
1 |
| 9 |
36.45 |
Sep |
1 |
| 11 |
35 |
Sep |
1 |
| 11 |
36.15 |
Sep |
1 |
| 12 |
34.05 |
Sep |
1 |
| 12 |
34.65 |
Sep |
1 |
| 12 |
35.4 |
Sep |
1 |
| 16 |
32.45 |
Sep |
1 |
| 17 |
36.55 |
Sep |
1 |
| 18 |
34 |
Sep |
1 |
Ignore the month at first and fit a simple linear regression to predict the PctDM based on the Age of the fish
A)Give an equation for the least squares line and comment on what it appears to indicate about the relationship between PctDM and Age
B)What percentage of the variability in PctDM does the Age explain for these fish?
C)Is there evidence that the relationship in part A is statistically significant? Explain how you know that it is or not
D)Produce a plot of the residuals versus the fits for the simple linear model. Does there appear to be any regular pattern?
E)Produce your plot from part D using points for each Month(Sept/Nov) with different symbols or colors. What do you observe about how the residuals might be related to the month? Now fit a multiple regression model, using an indicator (Sept, which is the forth column) for month and interaction product, to compare the regression lines for September and November.
F)Do you need both terms for a difference in intercepts and slopes? If not, delete any terms that aren't needed and run the new model.
G)What percentage of the variability in PctDM does the model in part F explain for these fish?
H)redo the plot in part E showing the residuals versus fits for the model in part F with different symbols for the months. Does this plot sho an improvement over your plot in part E? Explain