Answered: Consider the following population…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Consider the following population linear regression model of individual food

expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is

the individual’s age, and 50+0.5X is the population regression line. Suppose we

generate artificial data for 3 individuals using this model. This artificial sample, which

consists of 3 observations, is shown in the following table:

Answer the following questions. Show your working.

(a) What are the values of V1 and V4?

(b) Suppose we know that in this artificial sample, the sample covariance

between X and Y is 150, and the sample variance of X is 100. Compute the OLS

regression line of the regression of Y on X. (Hint: Assume these summary statistics

and the OLS regression line continue to hold in parts (c)-(e).)

Predicted value of Y
Observation
E(Y|X) u
Y
|(Yhat)
Residual (uhat)
1
20
V1
|-10
V4
V5
V7
2
30
V2
V3
70
V6
V8
3
40
70
10
80
81.67
|-1.67

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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