Capture a curvature in the relationship - quadratic model, Mathematics

1. Consider the model Yt = β0 + β1 Xt + εt, where t = 1,..., n.  If the errors εt are not correlated, then the OLS estimates of  β0  and β1  will be unbiased.

2. In the following regression model ln Yi = β0 + β1 X1i + β2 ln X2i + εi, all βk coefficients measure the elasticities of the Y variable with the respective X variables, because the Y variable appears in a logarithmic form. 

3. If we want to capture a curvature in the relationship between Yi and Xi, we have to use a quadratic model, where the slope is not constant everywhere and changes according to the value of Xi at which it is being assessed. 

4. If a hypothesis is rejected at the 0.10 level of significance, it may not be rejected at the 0.05 level of significance.

5. If β1  is positive in the equation 

(1)  Yi = β0 + β1 X1i + β2 X2i + εi, it can never be negative in the equation

(2)  Yi = β0 + β1 X1i + β2 X2i + β3 X3i + εi,.

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