Homework SourseA state fisheries commission wants to estimate the number of
A state fisheries commission wants to estimate the number of bass caught in a given lake during a season in order to restock the lake with the appropriate number of young fish. The commission could get a fairly accurate assessment of the seasonal catch by extensive “netting sweeps” of the lake before and after a season, but this techniques is too expensive to be done routinely. Therefore, the commission samples a number of lakes and records the following information.
• The seasonal catch measured in number of bass per square mile of lake area.
• Number of lake shore residences per square mile of lake area.
• Size of the lake in square miles
• Public access to the lake (= 1 if public have access, = 0 otherwise)
• Structure Index (Structure index is an index capturing living space for bass and include things like weed beds, sunken trees etc.)
The commission is convinced that the number of lake shore residences and the size of the lake are two important variables in predicting the seasonal catch. However, there is some question as to whether public accessibility to the lake and the Structure Index also contribute towards the prediction. The data file for the problem is Fish. a. Do a regression analysis to reflect the current conviction of the commission to see whether the number of lake shore residents and the size of the lake are good predictors. Comment on the results b. Do a second regression analysis to include one or more of the other variables. Comment on the results. You are looking for the best possible model.
| Seasonal Catch | No of lake shore residents | Size of the Lake | Public Access | Structure Index |
| 5400 | 138.3 | 0.315 | 0 | 81 |
| 1200 | 130.05 | 0.45 | 0 | 26 |
| 3750 | 120.3 | 0.465 | 0 | 52 |
| 4350 | 130.8 | 0.6 | 0 | 64 |
| 2100 | 97.35 | 0.66 | 0 | 40 |
| 1350 | 135.15 | 0.84 | 0 | 22 |
| 4800 | 91.05 | 1.17 | 0 | 80 |
| 4050 | 76.35 | 1.815 | 0 | 60 |
| 3300 | 129.15 | 0.51 | 1 | 30 |
| 8850 | 135 | 0.6 | 1 | 90 |
| 4950 | 120.6 | 0.78 | 1 | 74 |
| 4350 | 112.5 | 0.99 | 1 | 50 |
| 5400 | 105 | 1.17 | 1 | 61 |
| 3600 | 96.9 | 1.365 | 1 | 40 |
| 1350 | 75 | 1.65 | 1 | 22 |
| 3000 | 75 | 1.86 | 1 | 50 |
| 2850 | 76.8 | 2.205 | 1 | 37 |
| 4650 | 60.15 | 3.315 | 1 | 61 |
| 3900 | 67.5 | 3.69 | 1 | 39 |
| 5100 | 75 | 4.2 | 1 | 53 |
Solution
a) Do a regression analysis to reflect the current conviction of the commission to see whether the number of lake shore residents and the size of the lake are good predictors
Sol) The Regression equation is y=a+b(x1)+c(x2)
where y is seasonal catch
Using SPSS the regression model is
1760.805
a. Dependent Variable: catch
Hence The fitted regression is y =-1306.295+ (39.407) residents + (828.013) size
And the R sqaure value is 0.33. Hence 33% variation is due to size and residents.
b) Now we introduce other variables public and index then the Regression model is
Hence the regression model is y=-4176.0 + 26.8 (residents) +503.5 (size) +1114.39 (public) +76.69(index)
and r sqauare =0.956
Hence for Model 2 R sqaure value is high. Hence model 2 is best model
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
| 1 | .333a | .111 | .006 | 1760.805 |
