3. Consider a simple linear regression model (Y: Consumption, X: Disposable Income) Yị = $1 + 2X+ei according to the data (n = 10) given, we have n Σ(x − x)2 i=1 n i=1 X = Σ(Yi-Y)² n Y = 1 ΣΥ=70 Σy = 597 i=1 n i=30 ) X? =147 i=1 ΣXiYi i=1 n Σ? = 1.2 i=1 = n 57 = 107 1 i=1 n 3 ) X = i=1 n n 225, (X₁-X)(Y; - Y) = 15 i=1 (a) Obtain the estimates of 32 and 3₁ based on the numerical information given above. (b) Calculate the estimate of Var (32). (4) (c) Write down your fitted regression (estimated regression) model, and interpret the results. (d) Predict Yo value (the level of consumption) when the value of Xo (Income level) is given
3. Consider a simple linear regression model (Y: Consumption, X: Disposable Income) Yị = $1 + 2X+ei according to the data (n = 10) given, we have n Σ(x − x)2 i=1 n i=1 X = Σ(Yi-Y)² n Y = 1 ΣΥ=70 Σy = 597 i=1 n i=30 ) X? =147 i=1 ΣXiYi i=1 n Σ? = 1.2 i=1 = n 57 = 107 1 i=1 n 3 ) X = i=1 n n 225, (X₁-X)(Y; - Y) = 15 i=1 (a) Obtain the estimates of 32 and 3₁ based on the numerical information given above. (b) Calculate the estimate of Var (32). (4) (c) Write down your fitted regression (estimated regression) model, and interpret the results. (d) Predict Yo value (the level of consumption) when the value of Xo (Income level) is given
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
Related questions
Question
Transcribed Image Text:3. Consider a simple linear regression model (Y: Consumption, X: Disposable Income)
Y = Bi + B2Xite
according to the data (n = 10) given, we have
Y =
n
Σ(x − x)2
-
i=1
Σ
i=1
n
ΣΥ; - 1)2
i=1
ΣXiYi
i=1
ei = 1.2
X = 3 ΣX=30 Σx = 147
i=1
= 57
n
7 Y₁ = 70 Y² = 597
= 107
=
1
i=1
n
i=1
n
i=1
n
225, (X-X)(Y₂ - Y) = 15
i=1
(a) Obtain the estimates of 32 and 3₁ based on the numerical information given above.
(b) Calculate the estimate of Var (3₂).
(4)
(c) Write down your fitted regression (estimated regression) model, and interpret the results.
(d) Predict Yo value (the level of consumption) when the value of Xo (Income level) is given
by 12.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 14 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill