Weight Gain in Beef Cattle Production
Queensland is the largest grower of beef cattle in Australia. It is one of Queensland's leading industries and a major source of export income for the state.
The industry is very competitive due to both a large number of domestic suppliers as well as a number of other countries such as the United States who are also suppliers of high quality beef for the international market.
Many beef cattle growers have realised that the key to success in this industry is to be a low cost producer of good quality beef. As part of this process, many beef cattle growers have adopted a more scientific approach to herd management. In addition to traditional grass-fed animals, many beef producers have also introduced grain-fed animals where the animals are kept in a relatively confined area and fed a special diet of grain mixed with other nutrients such as molasses (a by-product of the sugar refining process). The animals are routinely weighed and their condition carefully monitored. Typical daily weight gains for feedlot animals ranges between 0.5kg to 2.5kg per day, while grass fed animals are somewhat lower than this.
The following data was collected from a small beef cattle company in Dallarnil in Queensland (approximately 300km north of Brisbane). The owners operate a 50 head feedlot on the property and also run around 80 head of cattle on the rest of the 80 hectare property. Twenty five head of cattle (steers) were purchased in late 1999 and grass fed on the property over an 18 month period.
The owners were interested in determining the typical weight gains the animals could obtain on this particular property. This information would be invaluable for determining the potential profits from their grass fed animals.Method
The 25 steers (de-sexed males) were purchased in September 1999 at an average age of 12 months. The animals were weighed on arrival to the property and their average weights entered on a database. Over the following 18 months the animals were routinely weighed and their weights entered. The data collected for the weights of the animals are shown in Table 1.
Table 1. Average weights per animal.Taking the average age of the animals to be 12 months, this data was converted to age (in days) and average weight per animal (kg). This data is shown in Graph 1 below:
Graph 1. Average Weight versus age of animal.
The population model describing the weight of the animals as a function of its age was defined as:
y is the weight of the animal in kilograms.
b 0 is the population intercept.
b 0 is the population slope.
x is the age of the animal in days.
e is the error term.
Regression analysis on the average weight per animal versus age was then performed using Microsoft Excel. A linear regression equation was then obtained in order to express the Average weight of the grass fed animals as a function of the animals age.
The regression output obtained from the data is shown below:
The sample regression equation obtained from the data was in the form of:
Using the results from the regression analysis, the regression equation describing the weight of the animal as a function of its age is given by:
This equation then allows us to estimate the weight of animal given its age in days.
The regression equation was then checked for adequacy by considering the standard error, testing the slope, and the coefficient of determination.
The standard error from the regression output was found to be 8.421. This figure is around 2.5% of the average y value of 343, suggesting the model was satisfactory.
The slope was then tested at a 5% level of significance. The null and alternative hypotheses for this test were:
H0: b 1 = 0
H1: b 1 > 0
The p-value (two-tailed) from the Excel output was 2.85x10-6 or 0.00000285. The p-value for the one tailed test was therefore approximately 1.43x10-6. Since the p-value was significantly less than the a value, the null hypothesis was rejected. It was concluded that there was very strong evidence to suggest that the slope was positive (as we would expect).
The last item from the regression output was the coefficient of determination which from the regression output was given as 0.979 or 97.9. This figure was considered to be excellent and suggested that 97.9% of the variation in the weight of the animal could be explained by its age.
Overall, the model selected was considered useful in determining the weight of a grass fed animal on the property. In addition, the residual plots from the regression output were considered.
The residual plot from the regression is shown below in Graph 2:
Graph 2. Residual Plot from Regression Output.
The regression output obtained was for time series data. One of the problems commonly encountered with time series data is auto-correlation where successive residuals are correlated with each other. In Graph 2 there is some evidence that auto-correlation may exist in this example.
The normal probability plot for the residuals is shown in Graph 3 below. The assumption used during the regression analysis is that the residuals are normally distributed around the mean. The results show the normal probability plot is reasonably linear, suggesting that our assumption is reasonable.
Graph 3. Normal probability Plot
The regression output found that the average weight gain for the grass-fed animals was linear over the age range examined. The resulting regression equation was found to be very useful in allowing the owners of the cattle property to predict the weight gains of the animals.
There was also some evidence of auto-correlation in the data. This would be expected given that rainfall varies throughout the year on the property and as such, the quality and quantity of the grass varies considerably. During the drier months (May to September), the cattle may fail to gain (or even lose) weight, while during the wetter months the animals tend to gain weight more rapidly.
Overall, the regression information was considered very useful in forecasting future cash-flows from the grass fed animals.