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 identical age and weight are purchased and brought to a feedlot. Each steer is fed a diet with a specific combination of antibiotic concentration (1=500mg/day, 2=1000mg/day) and percentage of feed supplement. The beginning weight (kg) of the steers is also recorded The data are as follows:

STEER ANIBIO SUPPLEM TIME

Steer	Weight	Antibiotic	Supplement	Time
1	300	1	3	88
2	250	1	5	82
3	425	1	7	81
4	458	2	3	82
5	222	2	5	83
6	325	2	7	75
7	115	1	3	80
8	365	1	5	80
9	245	1	7	75
10	500	2	3	77
11	210	2	5	76
12	195	2	7	72
13	231	1	3	79
14	321	1	5	74
15	269	1	7	75
16	200	2	3	74
17	317	2	5	70
18	251	2	7	69

(1a) What are your null and alternative hypotheses? (1b) What test did you conduct to address this question? Why? (1c) Did the data meet the assumption of your test? How did you verify this? If not, how did you deal with this? (1d) Is there a significant relationship between the time to being brought to the feedlot and the protein, antibiotic, and feed supplement? (1e) Which variables are significant in predicting time to market? Did each variable have a positive or negative impact on price?

Answer 1

1a) Null Hypothesis: Weight, Antibiotic and Supplement are not significant predictors of Time i.e Coefficients of all the three variables are zero in multiple regression equation i.e B1 = B2 = B3 = 0

Alternate Hypothesis: Atleast one of the coefficient is non-zero

1b) We will conduct a multiple regression analysis as we have three independent continuous variables and one dependent variables. Hence, it will tell us which variables are significant predictors and which are not.

1c) Assumptions of the test:

(i) The data collected is an independent random sample

(ii) The variables do not have any multicollinearity.

(iii) The relationship is linear between the independent and dependent variables.

We know first two are true and we could test the third assumption from the scatterplot. Hence, the data meets our assumptions.

1d) We can run the multiple regression with the independent variables being antibiotic and feed supplement on Excel. The output is as follows:

ANOVA
	df	SS	MS	F	Significance F
Regression	2	162.75	81.375	4.897192	0.023069
Residual	15	249.25	16.61667
Total	17	412

We can see that the overall model is significant and there is a significant relationship between the time and the protein, antibiotic and feed supplement.

1e) The output of the coefficient table is:

	Coefficients	Standard Error	t Stat	P-value
Intercept	90.20833	4.229184	21.32996	1.24E-12
Antibiotic	-4	1.921612	-2.08159	0.054923
Supplement	-1.375	0.588371	-2.33696	0.033722

If we take Alpha = 0.1 significance level, we can say that Antibiotic and supplement variables both are significant in predicting the time to market as p-value < 0.1 in both cases.

At alpha = 0.05, only the variable supplement is significant in predicting the time to market as p<0.05.

As the coefficients of both our variables are negative, we can say that both have a negative impact on the time to market.