1. Can you estimate a regression model for Y and X? 2. What are the assumptions of the model in 1? 3. Do you think that this model is accurate? 4. What are the related hypotheses of 3? 5. Discuss and interpret your results.
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- 2. Consider a two variable regression model, which satisfies all the Gauss Markov assumptions except that the error variance is proportional to X² i.e.E(u?) = o²X? Y₁ = B₁ + B₂X₁ + Ui How would you obtain the best linear unbiased estimates from the above regression.(2)What would the consequence be for a regression model if theerrors were not homoscedastic?What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?
- 1. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearity4. From the regression output, report the coefficients, standard errors, t-statistics, probability and R-squared (report the results in a table). 5. Re-write the specified model in (a) with values from the regression results and interpret the coefficients.10. Residual analysis Consider a regression of y on several independent variables, and the resulting predicted values of the dependent variable. The residual for the ith observation Consider a data set for a large sample of professional basketball players. Each observation contains the salary, as well as various performance statistics such as points, rebounds, and assists for each player. Suppose a regression of salary on all performance statistics is run, and the residuals are obtained. The player with the lowest (most negative) resid represents which of the following? (Assume the regression reasonably predicts salaries in most cases.) The most fairly paid player relative to her on-court performance The most overpaid player relative to her on-court performance The highest-paid player, regardless of her on-court performance The most underpaid player relative to her on-court performance
- Suppose that you had data on the amount of pollution in London every year. Write down the regression equation that you would need to estimate to measure the effect of ULEZ on pollution. Describe carefully what the dependent variable, the independent variable, the unit of observation (time or location), and the main coefficient of interest are. What control variables do you think should be included in this regression?Expedia wants to use regression analysis to build a model for airfare tickets prices in the states: Ticket prices = 30 + B1*Miles + E where Miles is measured in hundreds Coefficients 169.50 5.90 Intercept Miles (in hundreds) Which of the following is true? Standard Error 1.34 0.09 4 t Stat 126.85 61.28 P-value 0.000 0.002 If Miles increases by 1, then we predict ticket price to go up by $5.9. O If ticket price goes up by $1, then we predict Miles to go up by 590 miles. O If ticket price goes up by $100, then we predict Miles to go up by 590 miles. If Miles increases by 100, then we predict ticket price to go up by $5.9.In multiple regression model: what is it means for a variable to be significant? Explain the meaning of the significant variable.