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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