Question 36
A company has developed a new fodder for pigs. To model the “increase in weight of a piglet (in pounds) in one week”, an experiment is performed in which eight piglets were exclusively feed the fodder. Table-3 below provides the data on “Initial weight (pounds)”, “Age of the piglet (weeks)”, “Actual Weight gained after one week (pounds)” and “Predicted Weight gained after one week (pounds)” . The column "Predicted Weight gained after one week (pounds)" is obtained using Model-1
| Piglet Number | Initial Weight (pounds) | Initial Age (weeks) | Actual Weight Gained (pounds) | Predicted Weight Gained (pounds) |
|---|---|---|---|---|
| 1 | 39 | 8 | 7 | 6.1 |
| 2 | 52 | 6 | 6 | 5.8 |
| 3 | 49 | 7 | 8 | 6.3 |
| 4 | 46 | 12 | 10 | 10.0 |
| 5 | 61 | 9 | 9 | 9.1 |
| 6 | 35 | 6 | 5 | 4.1 |
| 7 | 25 | 7 | 3 | 3.9 |
| 8 | 55 | 4 | 4 | 4.5 |
Table-3
The different models developed are presented in the below Figures (which specify the partial regression outputs).
Given this information, answer the given subquestions
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | X1 |
| R Square | X2 |
| Adjusted R Square | X3 |
| Standard Error | |
| Observations | 8 |
ANOVA
| df | SS | MS | F | |
|---|---|---|---|---|
| Regression | X4 | |||
| Residual | ||||
| Total | X5 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | -4.2 | 1.89 | |
| Initial Weight (pounds) | 0.1 | 0.03 | |
| Initial Age (weeks) | 0.8 | 0.16 |
Model-1: Partial output when regression “Weight Gained (pounds)”, “Initial Weight (pounds)” and “Initial Age (weeks)”
ANOVA
| df | SS | |
|---|---|---|
| Regression | 450.76 | |
| Residual | 506.75 | |
| Total | 7 |
| Coefficients | ||
|---|---|---|
| Intercept | 44.65 | |
| Initial Age (weeks) | 0.09 |
Model-2: Partial output when regressing “Initial Weight (pounds)” and “Initial Age (weeks)”
ANOVA
| df | SS | |
|---|---|---|
| Regression | 22.5 | |
| Residual | 17.37 | |
| Total | 7 |
| Coefficients | ||
|---|---|---|
| Intercept | 7.22 | |
| Initial Weight (pounds) | 0.004 |
Model-3: Partial output when regressing “Initial Weight (pounds)” and “Initial Age (weeks)”
ANOVA
| df | SS | |
|---|---|---|
| Regression | 33.44 | |
| Residual | ||
| Total | 7 | 39.875 |
| Coefficients | ||
|---|---|---|
| Intercept | 5.52 | |
| Initial Weight (pounds) | 1.04 | |
| Weight Gained (pounds) | -0.11 |
Model-4: Partial output when regression “Weight Gained (pounds)”, “Initial Weight (pounds)” and “Initial Age (weeks)”
ANOVA
| df | SS | |
|---|---|---|
| Regression | 649.5 | |
| Residual | 308 | |
| Total | 7 | 957.5 |
| Coefficients | ||
|---|---|---|
| Intercept | 41.48 | |
| Initial Age (weeks) | -5.19 | |
| Weight Gained (pounds) | 6.5 |
Model-5: Partial output when regression “Weight Gained (pounds)”, “Initial Weight (pounds)” and “Initial Age (weeks)”
What is the value of the F-statistic for Model-1? (Note: Input your answer rounded to two decimal places. For example, if your answer is “1.235” then enter the answer as “1.24”)