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Assignment 5
STAT-S 320/520
Due on Jun 11, 2019
1. ISI 9.6 Problem 9.
2. ISI 9.6 Problem 12.
3. ISI 10.5 Problem Set C, Exercises 1-3.
4. ISI 11.4 Problem Set B, Exercises 2, 4, 6, 8, and 10.
5. ISI 11.4 Problem Set C, Problems 1 - 3.
6. The data Sahlins.txt that you can download from our Canvas page1
, were compiled by Sahlins (1972) from
information presented in Scudder’s (1962) report on the Gwenba valley of Central Africa. The data describe
agricultural production in Mazulu village. The explanatory variable (Consumers/Gardener) is the ratio of consumers
to productive individuals in each of 20 households, making suitable adjustments for the consumption requirements of
different household members. The response variable (Acres/Gardener) is a measure of domestic-labor intensity, based
on the amount of land cultivated by each household. Think of Consumers/Gardener as representing the relative
consumption needs of the household, and Acres/Gardener as representing how hard each productive individual in
the household works. Sahlins was interested in production, consumption, and redistribution of the social product in
“primitive” communities.
(a) Draw a scatterplot of Acres/Gardener (Y ) versus Consumers/Gardener (X). What relationship, if any, do you
discern in this plot –does the relationship appear to be positive or negative (or neither), linear or nonlinear,
strong or weak? Is there anything else noteworthy about the data– for example, do any households appear to
be unusual?
(b) Analyze the data by regressing Acres/Gardener (Y ) on Consumers/Gardener (Y ). In a society characterized by
“primitive communism, ”the social product of the village would be redistributed according to need, while each
household would work in proportion to its capacity, implying a regression slope of zero. In contrast, in a society
in which redistribution is purely through the market, each household should have to work in proportion to its
consumption needs, suggesting a positive regression slope and an intercept of zero. Interpret the results of the
regression in light of these observations. Examine and interpret the values of. Does the regression do
a good job of summarizing the relationship between Acres/Gardener and Consumers/Gardener?
(c) Find the standard errors of the intercept and slope. Can we conclude that the population slope is greater
than zero? Can we conclude that the intercept is greater than zero? Perform hypothesis tests to answer these
questions. Use some reasonable significance level and provide your conclusions.
(d) What do you expect to be the Acres/Gardener ratio for a household with a Consumers/Gardener ratio equal to
1.5. To answer this question, obtain an interval with a 95% confidence level.
7. Simulation: Assume the simple linear regression model
yi = β0 + β1xi + ei, i = 1, . . . , n where ei ~ N(0, σ2) for i = 1, . . . , n.
Let’s set β0 = 10, β1 = 2.5, and n = 30.
(a) Set σ = 100, and xi = i for i = 1, . . . , n.
(b) Your simulation will have 10,000 iterations. Before you start your iterations, set a random seed using your
birthday date (MMDD) and report the seed with your responses. For each iteration, obtain and store your
linear regression parameter estimates: (Include syntax. DO NOT include output)
(c) Using histogram and/or density plot, describe the distribution of . How do they compare with the true parameters, β0, β1, and σ2?
Briefly Explain. (Include syntax and output)
8. ISI 13.4 Problem 1.
9. ISI 13.4 Problem 11.
1The data and questions were constructed based on the supplementary material of “Applied Regression Analysis and Generalized Linear
Models” 3rd Ed by Fox.
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