2 Y; = 706 2 XiYi = 209,952 2 X² = 1,336,749 > Y² = 33,106 %3D %3D %3D i=1 i=1 i=1 i=1 A. Calculate X and Y 4478 706 ti9tI B. Calculate s C. Calculate Bo and Bi 179.12 25 28.24 222,527.L S401 104 Denoting the residuals from the estimated regression model by û,, show that the sum of the residuals equals zera 25, 2. L Σ-0 %3D i=1 Cxi-7)² Show that: Y = + û, Bo+B,X, %3D %3D is equivalent to: У; B,x, + û, where y, = Y-Y and x, Y,-Y and x, = X, - X %3D %3D %3D 4. Consider the estimated simple linear regression model Y, = B + B, X, + û, . Show that the estimated conditi %3D mean function fits through the sample means of the data. That is, show that Y = Y if X= X . %3D 5. Derive the least-squares estimators of the intercept ( B,) and slope (B) for the simple linear regression moc Show all steps for credit. 3.

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Hi, I need help with question 3. 

 

 

2 Y; = 706 2 XiYi = 209,952 2 X² = 1,336,749
> Y² = 33,106
%3D
%3D
%3D
i=1
i=1
i=1
i=1
A. Calculate X and Y
4478
706
ti9tI B. Calculate s
C. Calculate Bo and Bi
179.12
25
28.24
222,527.L
S401 104
Denoting the residuals from the estimated regression model by û,, show that the sum of the residuals equals zera
25,
2. L
Σ-0
%3D
i=1
Cxi-7)²
Show that:
Y = + û,
Bo+B,X,
%3D
%3D
is equivalent to:
У;
B,x, + û, where y, = Y-Y and x,
Y,-Y and x, = X, - X
%3D
%3D
%3D
4.
Consider the estimated simple linear regression model Y, = B + B, X, + û, . Show that the estimated conditi
%3D
mean function fits through the sample means of the data. That is, show that Y = Y if X= X .
%3D
5.
Derive the least-squares estimators of the intercept ( B,) and slope (B) for the simple linear regression moc
Show all steps for credit.
3.
Transcribed Image Text:2 Y; = 706 2 XiYi = 209,952 2 X² = 1,336,749 > Y² = 33,106 %3D %3D %3D i=1 i=1 i=1 i=1 A. Calculate X and Y 4478 706 ti9tI B. Calculate s C. Calculate Bo and Bi 179.12 25 28.24 222,527.L S401 104 Denoting the residuals from the estimated regression model by û,, show that the sum of the residuals equals zera 25, 2. L Σ-0 %3D i=1 Cxi-7)² Show that: Y = + û, Bo+B,X, %3D %3D is equivalent to: У; B,x, + û, where y, = Y-Y and x, Y,-Y and x, = X, - X %3D %3D %3D 4. Consider the estimated simple linear regression model Y, = B + B, X, + û, . Show that the estimated conditi %3D mean function fits through the sample means of the data. That is, show that Y = Y if X= X . %3D 5. Derive the least-squares estimators of the intercept ( B,) and slope (B) for the simple linear regression moc Show all steps for credit. 3.
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