Question

"A producer of various feed additives for cattle conducts a study of the number of days of feedlot time required to bring beef cattle to market weight. Eighteen steers of essentially identi- cal age and weight are purchased and brought to a feedlot. Each steer is fed a diet with a specific combination of protein content, antibiotic concentration, and percentage of feed supplement. The data are as follows:

STEER   PROTEIN ANIBIO  SUPPLEM TIME
1       10      1       3       88
2       10      1       5       82
3       10      1       7       81
4       10      2       3       82
5       10      2       5       83
6       10      2       7       75
7       15      1       3       80
8       15      1       5       80
9       15      1       7       75
10      15      2       3       77
11      15      2       5       76
12      15      2       7       72
13      20      1       3       79
14      20      1       5       74
15      20      1       7       75
16      20      2       3       74
17      20      2       5       70
18      20      2       7       69

2. Write the LS regression equation and interpret each of the (partial) slope parameter estimates, i.e., βˆ 1, βˆ 2 and βˆ 3.

3. For steer #3, Calculate the predicted feedlot time and the residual.

4. Write the residual standard deviation and interpret.

Answer 1

2. Ans: The LS regression equation and interpret each of the (partial) slope parameter estimates is
TIME = 90.7083 -5.1667 factor(PROTEIN)₁₅ -8.3333 factor(PROTEIN)₂₀ -4.0000 factor(ANIBIO)₂ -1.3750 SUPPLEM    Interpretation: When the Protein is 15, the mean of the time is 5.1667 less than the mean of time when Protein is 10. Similarly, when the Protein is 20, the mean of the time is 8.3333 less than the mean of time when Protein is 10.

When the Anibio is 2, the mean of the time is 4 less than the mean of time when Anibio is 1. Whereas, for a unit increase in supplement decrease the meantime by 1.3750.

3. The predicted feedlot time for steer #3 is

TIME = 90.7083 -5.1667 *0 -8.3333 *0 -4.0000 *0 -1.3750 *7 = 81.0833

and residual is 81-81.0833= -0.0833.

4.   The residual standard deviation is 1.685. The standard deviation of time condition on PROTEIN, ANIBIO, and SUPPLEM is 1.685.