Assume That the Data Looks as Follows:
Y = $\left( \begin{array} { l } Y _ { 1 } \\Y _ { 2 } \\O \\Y _ { n }\end{array}\right)$

question 14

Essay

Assume that the data looks as follows:
Y = $\left( \begin{array} { l } Y _ { 1 } \\Y _ { 2 } \\O \\Y _ { n }\end{array}\right)$ , U = $\left( \begin{array} { c } u _ { 1 } \\u _ { 2 } \\\mathrm { O } \\u _ { n }\end{array} \right)$ , X = $\left( \begin{array} { l } X _ { 11 } \\X _ { 12 } \\\mathrm { O } \\X _ { 1 n }\end{array} \right)$ , and β = (β₁)
Using the formula for the OLS estimator $\hat { \beta }$ = ( $X ^ { \prime }$ X)^-1
$X ^ { \prime }$ ^Y, derive the formula for $\hat { \beta }$ ₁, the only slope in this "regression through the origin."

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Definitions:

Volcanic Eruptions

The release of lava, ash, and gases from a volcano, which can have significant effects on the surrounding environment.

Correct Verb

The verb in a sentence that accurately matches its subject in number and tense, effectively conveying the action or state of being.

Tsunamis

Large, powerful sea waves caused by underwater earthquakes, volcanic eruptions, or other disturbances, capable of causing widespread destruction.

Correct Verb

The usage of the appropriate verb form that agrees with the subject in number and person and fits the sentence meaning.