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
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
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.
<
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. <
Expert Solution
steps

Step by step

Solved in 3 steps with 21 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman