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Regression analysis is a form of predictive modelling technique which investigates the relationship between a dependent i.e target and independent variable i.e predictor.
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- Consider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1E3A home appraisal company would like to develop a regression model that would predict the selling price of a house based on the age of the house in years (X1), the living area of the house in square feet (X2), and the number of bedrooms (X3). The following regression model was chosen using a data set of house statistics: y=88,399554791.3333x231,471.1372x3 The first house from the data set had the following values: Selling price $324,000 Age - 22 years Square Feet 2.000 Bedrooms 3 The residual for this house is 23,558 -41,480 10,216 -16,095 27
- 1. Consider the following regression model y = x3 + u. (1) Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss- Markov assumptions are: • MLR.1: The true model in the population is given by (1). • MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n} following the population model in (1). .... • MLR.3: No one explanatory variable can be written as a linear combination of the remaining explanatory variables that is, there is no perfectcollinearity. • MLR.4: In the population, the error u has an expected value of zero given any values of the explanatory variables, that is Elu|x] = 0. • MLR.5: In the population, the error u has the same variance given any values of the explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant. In the following scenarios, state whether B is an unbiased and consistent estimator of 3, and provide a brief justification for your answer in each case - but no formal mathematical…a) The R? should not be used to choose the best econometric model specification in multiple regression models. True or FalseEconometrics question
- b. The following model is a simplified version of the multiple regression model used by BEST Econometrics Group to study the trade off between time spent sleeping and working to look at other factors affecting sleep: sleep Bo + B₁totwrk + B₂educ + Page + μ₁ where sleep and totwork (total work) are measure in minutes per week and educ and age are measured in years. (i) If adults trade sleep for work, what is the sign of B₁? (ii) What signs do you think ₂ and 3 will have? (iii) Using the data in SLEEP75.RAW, the estimated equation is sleep = 3,638.25-.148totwrk-11.13educ - 2.20age, n = 706, R² = .113 If someone works five hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ (v) Would you say totwrk, educ, and age explain much of the variation in sleep? (vi) What other factors might affect the time spent sleeping? (vii) Are these likely to be correlated with totwrk?Define Interpretation of coefficients in polynomial regression models?46) The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the trade-off between time spent sleeping and working and to look at other factors affecting sleep: sleep = Bo + B₁totwrk + ß₂educ + ß3age +u, where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (i) If adults trade off sleep for work, what is the sign of f₁? (ii) What signs do you think ₂ and 3 will have? (iii) Using the data in SLEEP75, the estimated equation is sleep = 6,241.15 + 0.211totwrk + 9.22educ + 1.67age n = 211, R² = 0.981 If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ. (v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk?
- In 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?What are the various Standard errors in direct multiperiod regressions?In regression analysis, a common metric used in assessing the quality of the model being used to fit the data is known as the R-squared coefficient. Explain the R-squared coefficient. What is the difference between the R-squared and adjusted R-squared coefficients?
