Question 6. Table 2 presents data on the aggregate consumption (Y, in billions of HK dollars) and disposable income X, also in billions of HK dollars) for a developing economy over a 12-year period from 2012 to 2023. Year i Y₁ X₁ 2012 1 102 114 2013 2 106 118 126 2014 3 108 2015 4 110 130 122 136 124 140 128 148 2016 5 2017 6 2018 7 2019 8 130 156 2020 9 142 160 2021 10 148 164 O
Question 6. Table 2 presents data on the aggregate consumption (Y, in billions of HK dollars) and disposable income X, also in billions of HK dollars) for a developing economy over a 12-year period from 2012 to 2023. Year i Y₁ X₁ 2012 1 102 114 2013 2 106 118 126 2014 3 108 2015 4 110 130 122 136 124 140 128 148 2016 5 2017 6 2018 7 2019 8 130 156 2020 9 142 160 2021 10 148 164 O
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Related questions
Question

Transcribed Image Text:Question 6. Table 2 presents data on the aggregate consumption (Y, in billions of HK dollars)
and disposable income X, also in billions of HK dollars) for a developing economy over a 12-year
period from 2012 to 2023.
Year i Y₁ Xi
2012 1 102 114
2013 2 106 118
2014 3 108 126
2015 4 110 130
2016 5 122 136
2017 6 124 140
128
2019 8 130 156
2018 7
148
2020 9 142 160
2021 10 148 164
2022 11 150 170
2023 12 154 178
TABLE 2. Aggregate Consumption (Y) and Disposable Income (X)
Answer the following questions:
(1) Draw a scatter diagram using the data and visually inspect whether there exists an
approximate linear relationship between Y and X.
(2) Determine the simple regression equation for the consumption schedule in Table 2, using
«ΣΧΥ - ΣΧ ΣΥ
to find ₁ and Bo=Y - B₁X to find Bo.
nΣX - (ΣΧ.)2
3₁
(3) (Optional) Plot the simple regression line and illustrate the deviations of each Y; from
the corresponding Y₁.
(4) For the aggregate consumption-income observation in Table 2, use the results from (2)
to compute
(b) s
(c) s²₁
(5) Use the results from (2) to computer for the estimated consumption regression using
the following methods:
MMAT5330 Econometric Principles and Data Analysis
(a) √R²
(b) r =
(c) r =
Σ xiyi
√[x²√Σy?
where x₁ =
B₁
ΣXi Yi
Σy
X₁ - X, and y₁ = Yį – Y.
(6) Derive the following:
(a) Starting with ₁
«ΣΧΥ - ΣΧ ΣΥ
«ΣX - (ΣΧ.)2
derive the equation for ₁ in deviation
form for the case where X = Y = 0.
(b) Determine the value of Bo=Y-B₁X when X = Y = 0.
(c) (Optional) Use the results of (a) and (b) to plot the simple regression line on a
graph where the variables are measured as deviations from their respective means.
Compare this simple regression line with the simple regression line plotted in (3)
on the same graph.
<
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