[SOLVED] R STA 304H1F-1003H Fall 2019

STA 304H1F-1003H Fall 2019
Assignment 2-Question 3 Question 3. ( 18 marks)
A certain manufacturing firm produces a product that is packaged under two brand names, for marketing purposes. These two brands serve as strata for estimating potential sales volume for the next quarter. A SRS of customers for each brand is contacted and asked to provide a potential sale figure y (in number of units) for the coming quarter. Last years true sales figure, for the same quarter, is available for each of the sampled customers and is denoted by x. The data are given in the accompanying table. The sample for brand I was taken from a list of 120 customers for whom the total sales in the same quater of last year was 24,500 units. The brand II sample come from 180 customers with a total quarterly sales last year of 21 200 units.
Brand I Brand II
xi yi xi yi 204 210 137 150 143 160 189 200
82 75 119 125 256 280 63 60 275 300 103 110 198 190 107 100
159180
63 75
87 90
Use R to do the following questions. Please, use the R-output to answer question. The R command should be reported in an eppendix. It worse 2 marks.
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(Part 1)
(10 marks) Using Separate Ratio Estimator Method (SR)
(a) (2 marks) Find a basic estimate (without auxiliary information) of the total potential sales. Estimate the variance of your estimator.
(b) (2 marks) Find a ratio estimate of the total potential sales. Estimate the variance of your estimator.
(c) (2 marks) Find a regression estimate of the total potential sales. Estimate the variance of your estimator.
(d) (3 marks) Compute the relative efficiency of
(i) ratio estimation to basic estimation
(ii) ratio estimation to regression estimation
(iii) regression estimation to basic estimation
(e) (1 mark) Which method of estimation do you recommend?
(6 marks) Using Combined Ratio Estimator Method (CR)
(a) (2 marks) Find a basic estimate (without auxiliary information) of the mean potential sales. Estimate the variance of your estimator.
(b) (2 marks) Find a ratio estimate of the mean potential sales. Estimate the variance of your estimator.
(d) (1 mark) Compute the relative efficiency of ratio estimation to basic estimation
(e) (1 mark) Which method of estimation do you recommend?
(Part 2)
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