Given $\begin{array} { c c } \frac { \mathrm { Yi } } { 5.5 } & \frac { \mathrm { Xi } } { 3.5 } \\14 & - 1.2 \\- 10 & - 2.3 \\11 & 7.8\end{array}$
Y_i = $\hat { \beta } _ { 0 }$ - $\hat { \beta } _ { 1 }$
X_i + e_i $\hat { \beta } _ { 0 }$ = 2.97
$\hat { \beta } _ { 1 }$ = 1.10
Calculate the value of the four e_i's.
Show your work making the details of your calculations apparent."

Question

Given

\begin{array} { c c } \frac { \mathrm { Yi } } { 5.5 } & \frac { \mathrm { Xi } } { 3.5 } \\14 & - 1.2 \\- 10 & - 2.3 \\11 & 7.8\end{array}

Y_i =

\hat { \beta } _ { 0 }

-

\hat { \beta } _ { 1 }

X_i + e_i

\hat { \beta } _ { 0 }

= 2.97

\hat { \beta } _ { 1 }

= 1.10
Calculate the value of the four e_i's.
Show your work making the details of your calculations apparent."

Quizplus · Accepted Answer

The Answer is ei = Yi -

\hat { Y } _ { i }

= Yi - (

\hat { \beta } _ { 0 }

+

\hat { \beta } _ { 1 }

Xi) = 5.5 - (2.97 + (1.10 x 3.5)) = -1.33 (6.38)
ei = Yi -

\hat { Y } _ { i }

= Yi - (

\hat { \beta } _ { 0 }

+

\hat { \beta } _ { 1 }

Xi) = 14 - (2.97 + (-1.10 x -1.2)) = 12.35 (9.71)
ei = Yi -

\hat { Y } _ { i }

= Yi - (

\hat { \beta} _ { 0 }

+

\hat { \beta } _ { 1 }

Xi) = -10 - (2.97 + (-1.10 x -2.3)) = -10.44 (-15.50)
ei = Yi -

\hat { Y } _ { i }

= Yi - (

\hat { \beta } _ { 0 }

+

\hat { \beta } _ { 1 }

Xi) = 11 - (2.97 + (-1.10 x 7.8)) = -0.58 (16.61)

Given Yi5.5Xi3.514−1.2−10−2.3117.8\begin{array} { c c } \frac { \mathrm { Yi } } { 5.5 } & \frac { \mathrm { Xi } } { 3.5 } \\14 & - 1.2 \\- 10 & - 2.3 \\11 & 7.8\end{array}5.5Yi​14−1011​3.5Xi​−1.2−2.37.8​