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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.

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

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.

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