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

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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.
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.
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