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).) (c) What are the values of V5 and V7?

MATLAB: An Introduction with Applications
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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).)
(c) What are the values of V5 and V7?
 
 
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
Transcribed Image Text: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
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