LRM, averages
Problem
a) Show that it will follow from the linear regression model \(y_i=β_1+β_2x_i+ε_i\) that
\[\bar{y}=β_1+β_2\bar{x}+\bar{ε}\]
b) Show that
\[y_i-\bar{y}=β_2\left( x_i-\bar{x} \right)+ε_i-\bar{ε}\]
Solution
Problem
a) Show that it will follow from the linear regression model \(y_i=β_1+β_2x_i+ε_i\) that
\[\bar{y}=β_1+β_2\bar{x}+\bar{ε}\]
b) Show that
\[y_i-\bar{y}=β_2\left( x_i-\bar{x} \right)+ε_i-\bar{ε}\]
Solution