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:

Self-Esteem

An individual's subjective evaluation of their own worth and capabilities.

Intergroup Bias

The tendency to favor one's own group over other groups in terms of judgment, preference, or treatment.

Task Conflict

Disagreements about the nature of the work to be done.

Relationship Conflict

Interpersonal tensions among individuals that have to do with their relationship per se, not the task at hand.