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List the 5 assumptions of the Classical Linear Regression Model and explain at least three of them
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- According to Environmental Kuznets curve, it is expected that there is an Inverse-U shape relationship between pollution and real income such that the following quadratic functional form (regression model) must be specified: Y = a1 + a2 X + a3 X² + u where the variables Y and X represent respectively air pollution (CO2) and real income (RGDP). u is the random error. a) Suppose a researcher wants to investigate the relationship between pollution and real income by defining a linear functional form such as Y = B1+ B2 X+e. Show technically how you test whether quadratic form or linear form is the correct model specification using Ramsey's Reset test. b) Suppose R² is found 0.75 from quadratic form, 0.55 from linear form and 0.73 from the auxiliary regression. Given n=35, carry out Reset test and interpret the result. c) Suppose you found out that the correct specification is the quadratic regression. In this case, would estimating the linear functional form result in an unbiased estimate…How to include dummy variables in a regression? Give an exampleImagine you are an economist working for the Government of Econville. You are tasked with developing a model to predict the GDP of the country based on various factors such as interest rates, inflation, unemployment rate, and population growth. You collect quarterly data for the past 20 years and start building your model. After running your initial regression, you notice some peculiar patterns in the residuals: (1) residuals do not have identical variances across different levels of the independent variables; (2) two or more independent variables in a regression model are highly correlated with each other; (3) the correlation of a variable with its own past values. You suspect that your model might be suffering from 3 potential issues in the regression analysis that can affect reliability and validity. what are the implications of Heteroscedasticity if this potential issue in your model?
- What are the commonalities and differences between regression and correlation?Imagine you are an economist working for the Government of Econville. You are tasked with developing a model to predict the GDP of the country based on various factors such as interest rates, inflation, unemployment rate, and population growth. You collect quarterly data for the past 20 years and start building your model. After running your initial regression, you notice some peculiar patterns in the residuals: (1) residuals do not have identical variances across different levels of the independent variables; (2) two or more independent variables in a regression model are highly correlated with each other; (3) the correlation of a variable with its own past values. You suspect that your model might be suffering from 3 potential issues in the regression analysis that can affect reliability and validity. List 2 factors in your model that might be causing the Heteroscedasticity and give a reasonProve that the slope of the sample regression function (beta2) is the BLUE if the assumptions of Gauss Marko theorem are satisfied make sure to show all the steps and the underlying assumptions
- Explain why in every econometric model there must be an error term, explain its function.Imagine you are an economist working for the Government of Econville. You are tasked with developing a model to predict the GDP of the country based on various factors such as interest rates, inflation, unemployment rate, and population growth. You collect quarterly data for the past 20 years and start building your model. After running your initial regression, you notice some peculiar patterns in the residuals: (1) residuals do not have identical variances across different levels of the independent variables; (2) two or more independent variables in a regression model are highly correlated with each other; (3) the correlation of a variable with its own past values. You suspect that your model might be suffering from 3 potential issues in the regression analysis that can affect reliability and validity. Based on Addressing Heteroscedasticity list one test you would employ to test this potential issue?7. The Stata data set "college_gpa" has data on students' college GPAS, high school GPAS, ACT scores, lectures skipped during the academic year, and other characteristics. We wish to examine the predictors of college GPAS. You must submit your do-file (commands). a) Regress college GPA on high school GPA and write the estimated regression line. b) Interpret the intercept of your regression in a sentence. Does this coefficient make sense?n Explain c) Interpret the coefficient on high school GPA in a sentence. Does this coefficient make sense? Explain. reg colGPA hsGPA Source df MS Number of obs 141 %3D F(1, 139) 33.80 Model 5.58478164 1 5.58478164 Prob > F e.0000 Residual 22.9668501 139 .165229138 R-squared Adj R-squared 0.1956 %3D 0.1898 %3D Total 28.5516318 140 .203940227 Root MSE .40648 colGPA Coef. Std. Err. t P>|t| [95% Conf. Interval] hsGPA .6242948 .1073816 5.81 0.000 .4119822 .8366073 _cons 890254 3669263 2.43 0.017 647755
- Please answer all three sub-sections of this questionIn multiple regressions, the correlation coefficient of each independent variable can be measured in addition to the multiple correlation coefficient. How do the values of individual correlation coefficients compare to the value of the multiple correlation coefficient?Consider the following regression model: wage-Bi+Bamalerpumalexedu Buedutu, where wage is the hourly wage measured in dollars: male is a dummy variable for males edu is the years of education: maleedu is the interaction of male and edu variables. The parameter estimates for B parameters are P-1.27: B1.29: Br-0,16: Be-0.82. What is the predicted marginal effect of years of education for males?
