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Econometrics Tutor Columbia University New York, NY

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The linear regression model is given by Consumption_i=\alpha + \beta Income+\epsilon_i,   i=1, 2, 3, ..., n

  • Consumption_i is the dependent variable,
  • Income_i is the independent variable,
  • \alpha is the intercept,
  • \beta is the slope,
  • \epsilon_i is the error term
  • n is the sample size

The resulting estimators for \alpha and \beta, denoted by \hat{\alpha} and \hat{\beta} are derived using the OLS technique.

Econometrics Tutor Columbia New York OLS estimators

OLS Estimators

OLS predicted values \hat{Y_i}=\hat{\beta_0} + \hat{\beta_1}X_i,  \hat{\epsilon_i}= Y_i + \hat{Y_i}

Question: what is the difference between \hat{\epsilon_i} and \epsilon_i

R-Squared is the ratio of ESS to TSS

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R-squared explains the proportion of variation in data explained by the model. Higher R-squared implies that our model is able to explain a higher proportion of variation in the dependent variable.

Columbia University Econometrics Tutors Lecture 1
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New York Econometrics Tutors online Lecture 3
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