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What is the Role of Control Variables in Multiple Regression?
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- what are the key features , Strength and limitation of following model? and when which model should be used? Ordinary Least Squares Logit regression model Probit regression modelWhat assumption is violated when multicollinearity is present in the regression model?In a multiple OLS regression. Does correlation between explanitory variables violate assumtion number 4 multicolliniearity? Or is it just for perfect colinearity?
- Kristin Forbes in her American Economic Review (2000) article investigates the relationship between economic growth and inequality. She uses five yearly data for 45 countries for the time period 1965-1995. In the table below are results of her using four types of panel regression estimation techniques for the same model, where she estimates the relationship between economic growth and inequality (measured by the Gini coefficient) Estimation method Inequality Income Male Education Female Education PPP R² Countries. Observations Period Fixed effects (1) 0.0036 (0.0015) -0.076 (0.020) -0.014 (0.031) 0.070 (0.032) -0.0008 (0.0003) 0.67 45 180 1965-1995* Five-year periods Random effects (2) 0.0013 (0.0006) 0.017 (0.006) 0.047 (0.015) -0.038 (0.016) -0.0009 (0.0002) 0.49 45 180 1965-1995 Chamberlain's 77-matrix (3) 0.0016 (0.0002) -0.027 (0.004) 0.018 (0.010) 0.054 (0.006) -0.0013 (0.0000) 45 135 1970-1995 Arellano and Bond (4) 0.0013 (0.0006) -0.047 (0.008) -0.008 (0.022) 0.074 (0.018)…The tables to the right give price-demand and price-supply data for the sale of soybeans at a grain market, where x is the number of bushels of soybeans (in thousands of bushels) and p is the price per bushel (in dollars). Use quadratic regression to model the price-demand data and linear regression to model the price-supply data. Complete parts (A) and (B) below. (A) Find the equilibrium quantity and equilibrium price. The equilibrium quantity is thousand bushels. (Round to three decimal places as needed.) Price-Demand p = D(x) 6.59 6.48 6.38 6.27 6.24 (Round to the nearest dollar as needed.) X 0 10 20 30 40 The equilibrium price is $ per bushel. (Round to the nearest cent as needed.) (B) Use a numerical integration routine to find the consumers' surplus and producers' surplus at the equilibrium price level. The consumers' surplus is $ (Round to the nearest dollar as needed.) The producers' surplus is $ Price-Supply p = S(x) 6.40 6.47 6.53 6.54 6.61 X 0 10 8888 20 30 40If we suppose that the weekly price of milk is $3.40 per gallon and MPEP changes the weekly advertising to $300, the best-fitting regression model to estimate the weekly quantity of milk consumed would be Q = 6.52 - 1.614 (3.40) + .005 (300) = 2.533 gallons of milk. What is the elasticity between $5 and $4? Should you lower or raise price to maximize revenue?
- Which of the following is true of the White test? a. The White test is used to detect the presence of multicollinearity in a linear regression model. b. The White test assumes that the square of the error term in a regression model is uncorrelated with all of the independent variables, their squares, and cross products. c. The White test cannot detect forms of heteroscedasticity that invalidate the usual ordinary least squares standard errors. d. The White test can detect the presence of heteroscedasticity in a linear regression model even if the functional form is misspecified.QUESTION 2 Continue to use the example from Question 1. Suppose each product is randomly assigned to a process by a computer program, but some products get reassigned on the factory floor (for practical reasons). Let Z¡ denote the original assignment and X¡ the actual process used to produce i. In a regression of Y¡ on X¡ and Wj, OLS is: d. Potentially biased because W; should not be included b. Potentially biased, but an IV regression using Z¡ as an instrument can be used to obtain a consistent estimator C. Unbiased because the products were randomly assigned in the beginning d. Unbiased as long as Zj is also included as a control variableSuppose 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 r²
- List the 5 assumptions of the Classical Linear Regression Model and explain at least three of themChildren who were breastfed as infants have higher average IQs on average than children who were not. Breastfeeding advocates claim that this is due to the superior nutrition in breastmilk including brain building chemicals such as DHA. You have been hired to investigate this relationship more fully. Your employers are worried about the possibility of omitted variables biasing the results of the study. Name 3 possible omitted variables and explain how they might bias the results. Explain 2 empirical strategies you might use in your investigation.Using data from a random sample of 1000 working adults, we obtain the following estimated regression to study the effect of experience (exper) on log of wage (log(wage)). log(wage) = 5.423 -0.034ezper +0.009ezper² + 0.082educ + 0.157male What other regression do you need to run to test the null hypothesis that, holding other factors fixed, experience has no effect on log(wage)? Explain what test you would perform.
