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日期:2019-06-13 10:13

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.

1


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