**Question:** Estimate the regression equation ๐ = ๐ฝ0 + ๐ฝ1๐1 + ๐ฝ2๐2 +๐ฝ3๐3 +๐ via ordinary least squares (2 marks).

29 Apr 2023,9:59 PM
**Section** **A:** **Ordinary** **Least** **Squares** **(****400** **words,** **12** **marks)**

Estimate the regression equation ๐ = ๐ฝ + ๐ฝ ๐ + ๐ฝ ๐2 + ๐ฝ ๐3 + ๐ via ordinary least squares (**2** **marks**). Interpret all regression coefficients and assess their statistical significance using a T-test (**4** **marks**). Discuss the explanatory power of the model using the R-squared and the F-test (**2** **marks**). Briefly explain the implications of documented relationships or lack thereof for theory and practice in context of relevant academic sources (4 **marks**).

**Section** **B:** **D****iagnostic** **Tests** **(800** **w****ords,** **24** **marks)**

Discuss the assumptions you used when performing an ordinary least squares regression (**4** **marks**). Formally test for any **THREE** **(3)** different assumption violations using appropriate statistical procedures, justifying and critically evaluating these using relevant literature (**15** **marks**). Briefly discuss the implications of the results for model validity (**5** **marks**). In this section, you can address concepts such as, for example, autocorrelation, heteroskedasticity, multicollinearity, endogeneity, heterogeneity, or omitted variable bias.

**Section** **C:** **Robustness** **Checks** **(800** **words,** **24** **marks)**

Perform **ONE** **(1)** robustness check of your choice for your model. Present the procedure using necessary equations, tables, and figures, and referencing appropriate academic sources (**15** **marks**). Discuss the relevance of the robustness test employed in relation to model and diagnostic test results (**5** **marks**). Compare the coefficients qualitatively and quantitatively to those obtained from ordinary least squares (**4** **marks**). In this section, you can address concepts such as, for example, subsample estimations, structural shifts, robust standard errors, weighted least squares, autoregressive models, GARCH, quantile regression, ridge regression, or LASSO.

https://apaxresearchers.com/storage/files/2023/04/29/9667-ZEm_19_58_57_af5039-assignment-brief-22-23.pdf

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