Basic models: linear regression Econometrics

okun s law representing relationship between gdp growth , unemployment rate. fitted line found using regression analysis.

for example, consider okun s law, relates gdp growth unemployment rate. relationship represented in linear regression change in unemployment rate (



Δ
 

unemployment



{\displaystyle \delta \ {\text{unemployment}}}

) function of intercept (




β

0




{\displaystyle \beta _{0}}

), given value of gdp growth multiplied slope coefficient




β

1




{\displaystyle \beta _{1}}

, error term,



ε


{\displaystyle \varepsilon }

:

Δ
 

unemployment

=

β

0


+

β

1



growth

+
ε
.


{\displaystyle \delta \ {\text{unemployment}}=\beta _{0}+\beta _{1}{\text{growth}}+\varepsilon .}

the unknown parameters




β

0




{\displaystyle \beta _{0}}

,




β

1




{\displaystyle \beta _{1}}

can estimated. here




β

1




{\displaystyle \beta _{1}}

estimated −1.77 ,




β

0




{\displaystyle \beta _{0}}

estimated 0.83. means if gdp growth increased 1 percentage point, unemployment rate predicted drop 1.77 points. model tested statistical significance whether increase in growth associated decrease in unemployment, hypothesized. if estimate of




β

1




{\displaystyle \beta _{1}}

not different 0, test fail find evidence changes in growth rate , unemployment rate related. variance in prediction of dependent variable (unemployment) function of independent variable (gdp growth) given in polynomial least squares.