Problem 2: Consider a data set consisting of observations on i = 1,... ,n units over t = 1,...,T time periods and suppose that n is large and T is small (e.g., you have n = 5000 patients observed over T = 10 years). Write down an econometric model that can be used to analyze the data and explain its components. What problems arise if in your regression you ignore the fact that patients are potentially heterogeneous? Show an example of this graphically. Discuss one approach to estimating the parameters of this model, listing the necessary steps.
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- Suppose you have run four regression models: A, B, C, and D. You are going to make a decision on which one to use just based on the adjusted r² value. Here are the adjusted r² values for each model: A: 0.71 B: 0.57 C: 0.65 D: 0.76 Which regression model would you choose based on the adjusted r²? OD since it has the highest adjusted r² value B since it has the lowest adjusted r² OC since it has an adjusted r² between the adjusted r² of regressions B and D. Either B or C since they have the lowest adjusted r²Having successfully completed your first year in university, you began your second year with an evaluation of your past performance. You observed that you performed well in those subjects where you were diligent with class attendance whilst you performed poorly in those courses where you missed a number of classes. Upon learning about OLS regression you realize that you are able to predict your average performance based on the number of classes attended. The table below shows your data set. Number of Lectures (X) Percentage Scored (Y) 1 30 2 45 3 51 4 57 5 60 6 65 7 70 8 71 9 72 10 73 11 66 12 71 13 47 14 81 15 83 16 84 17 89 18 99 19 82 20 86( TRUE OR FALSE help me find the true or false questions ) 1. In economic statistics and Econometrics, we do the same thing.( ) 2. As same in regression analysis, variables in relation analysis are all random variables.( ) 3. Known as residual, "i is an estimate of u , the random disturbance term.( ) 4. The slope coefficient of the log-log model measures the elasticity of Y with respect to X.( ) 5. In regression of standardized variables, the intercept term is always zero.( ) 6. The underlying theory may suggest a particular functional form.( ) 7. The disturbance term u is assumed to follow normal distribution.( ) 8. White test is used to check if there exists multicollinearity in the disturbance term of a regression function.( ) 9. Dummy variable can be used to test the stability of a regression model just as the function of the Chow Test.( ) 10. Where there is autocorrelation in the u , the OLS estimators are not BLUE estimators any more.( )
- Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatterplots and using economic theory, the economist decides to estimate an equation of the form Q= aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = - 1.3. Now consider two scenarios: (1) the price increases from $10 to $12.50; (2) the price increases from $20 to $25. a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not? b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2? Be as exact as possible.Issues of multicollinearity impacted the ‘validity and trustworthiness’ of a regression model. Demonstrate how this issue can be a problem by using appropriate hypothetical example.What are the most important remaining threats to the internal validity of this regression analysis?
- A realtor was investigating the price of real estate based on the size of the house in square feet x1 and if the house was within walking distance of an "A" rated public school. The indicator variable is defined as x = 1 if the house is within walking distance of an "A" rated public school and x = 0 if the house is NOT within walking distance of an "A" rated public school. If there was interaction in the regression problem, an appropriately fit regression model would have…? a) A different slope and different y-intercept for those within walking distance and those not. b) A different y-intercept for those that were within walking distance and those that were not; the slope would not change. c) A different slope, but not a different y-intercept for those within walking distance and those not. d) Cannot be determinedtate whether the following statements are true or false with a brief explanation: a) Logit model is estimated by minimising the sum of the squares residuals of the model. b) In difference-in-differences analysis, the assumption of ‘parallel trends’ is generally testable. c) Suppose you have estimated a model Y = 0.2 – 0.7D + 2X + 0.4X*D. Y and X are continuous variables and D is a dummy variable. If D=1, the marginal effect of X on Y is always larger, and therefore the predicted Y is always larger, than in the case where D=0. d) The first order autoregressive model can be stationary or non-stationary. e) The bias in Instrumental Variables estimator depends on the number of observations.Write (TRUE/FALSE) for each question. An observation with a large standardized residual value always generates a large Cook’sdistance value. (T/F)Leverage value detects unusual x values. (T/F)BIC gives heavier penalty on models with many variables than Cp or AIC. (T/F) As the tuning parameter λ → ∞, the coefficients of ridge regression tend to zero. (T/F)Like the least square coefficient, ridge regression coefficients are scale equivalent. (T/F)The shrinkage penalty is applied to all coefficient except for the intercept. (T/F) Lasso regression reduces the bias by increasing the tuning parameter. (T/F)
- What are the measures of fit that are commonly used for multiple regressions? How can an adjusted R2 take on negative values?Which one of the following is NOT an assumption of the classical linear regression model (CLRM)? Select one: a. The disturbance terms are independent of one another. b. The dependent variable is not correlated with the disturbance terms. c. The explanatory variables are uncorrelated with the error terms. d. The disturbance terms have zero mean.Literacy rate reflects the educational facilities and quality of education available in a country, and mass communication plays a large part in the educational process. To relate the literacy rate of a country to various mass communication outlets, a demographer has proposed to relate literacy rate to the following variables: News = number of daily newspaper copies (per 1000 population) Radio = number of radios (per 1000 population) TV = number of TV sets (per 1000 population). The regression model to estimate the literacy rate (?̂ ) is below: ?̂= 0.5149 + 0.0005*News - 0.0003* TV + 0.002* Radio Answer the following questions: 4.1) Interpret the coefficient value of the TV variable in the model. 4.2) Predict the literacy rate for a country that has 200 daily newspaper copies (per 1000 in the population), 800 radios (per 1000 in the population), and 250 TV sets (per 1000 in the population). Show a detailed solution to support your answer.