Question

Proportion at 77mm (%)	Average Rainfall	Hand Feeding
67	100	1
75	150	0
80	148	0
72	70	1
91	210	0
69	120	1
55	50	1
77	167	0
84	230	0
92	189	0
58	40	1
69	93	1
74	133	0
72	80	1
66	108	1

A farmer who specialises in the production of carpet wool where the sheep are shorn twice per year is seeking a 75-mm-length clip from his Tukidale sheep. He believes that the proportion of sheep at each clip meeting this standard varies according to average rainfall during the six-month growing period and whether additional hand feeding of high protein sheep nits occurs during the period (because of a shortage of grass cover in the paddocks). Hand feeding is measured as 1 and no hand feeding as 0. Showing ALL formulas and working;

a) Predict the proportion at 75mm if the rainfall is 180 mm and there is no hand feeding, a construct a 95% confidence interval estimate and 95% prediction interval.

b) Is there a significant relationship between the clip length proportion and the two independent variables at the 0.05 level of significance?

c) Construct 95% confidence interval estimates of the population slope for the relationship between clip proportion and rainfall, and between clip proportion and hand feeding.

d) Interpret the meaning of the coefficient of multiple determination.

e) Calculate the coefficients of partial determination and interpret their meaning.

f) Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.

Answer 1

Using Minitab software, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

a) Using Minitab software, (Stat -> Regression -> Regression -> Predict), we get the following output :

b) Testing the significance of the relationship between the clip length proportion and the two independent variables at the 0.05 level of significance,

The value of the test statistic F = 23.24

and P-value = 0

Since P-value = 0 < 0.05, so at 5% level of significance we can conclude that there is significant relationship between the clip length proportion and the two independent variables.

c) Here

estimated slope

standard error of slope

and sample size n = 15

a 95% confidence interval estimates of the population slope for the relationship between clip proportion and rainfall

a 95% confidence interval estimates of the population slope for the relationship between clip proportion and hand feeding

d) The coefficient of multiple determination

79.48% variation in the proportion at 77 mm can be explained by the above regression equation.