Consider the Following Population Regression Function: Y = X $\left[ \begin{array} { l } Y _ { 1 } \\Y _ { 2 } \\\ldots \\Y _ { n }\end{array} \right]$

question 47

Essay

Consider the following population regression function: Y = X? + U
where Y= $\left[ \begin{array} { l } Y _ { 1 } \\Y _ { 2 } \\\ldots \\Y _ { n }\end{array} \right]$ , X= $\left[ \begin{array} { l l } 1 & X _ { 1 } \\1 & X _ { 2 } \\\ldots & \ldots \\1 & X _ { n }\end{array} \right]$ , ? = $\left[ \begin{array} { l } \beta _ { 0 } \\\beta _ { 1 }\end{array} \right]$ , U= $\left[ \begin{array} { c } u_1 \\u_2 \\\ldots \\u_\text{n}\end{array} \right]$ Given the following information on population growth rates (Y)and education (X)for 86 countries $\sum _ { i = 1 } ^ { n } Y _ { i } = 1.594$ , $\sum _ { i = 1 } ^ { n } x _ { i } = 449.6$ , $\sum _ { i = 1 } ^ { n } Y _ { i } ^ { 2 } = 0.03982$ , $\sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } = 3,022.76$ , $\sum _ { i = 1 } ^ { n } x _ { i } Y _ { i } = 6.4697$ a)find X'X, X'Y, (X'X)^-1 and finally (X'X)^-1 X'Y.
b)Interpret the slope, and if necessary, the intercept.

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Definitions:

Postoperative Period

The recovery phase following surgery, involving monitoring, pain management, and care to ensure proper healing.

Morphine

A powerful opioid pain medication derived from opium, used to relieve severe pain.

Methadone

A synthetic opioid used for pain management and as part of medication-assisted treatment to reduce withdrawal symptoms and cravings in people with opioid use disorder.

Codeine

An opiate used to treat pain or cough, and it is known for its analgesic effects.