In a regression problem with 1 output variable and with a total number of 100 possible input variables, what is the number of all possible models with three input variables?
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In a regression problem with 1 output variable and with a total number of 100 possible input variables, what is the number of all possible models with three input variables?
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- In a regression problem with one output variable and one input variable, we set up two cutpoints z1 and z2 for the input variable and we fit a step function regression model based on these two cutpoints of the input variable. If you write the regression problem in matrix form y = X%*%β + ε, how many rows would the vector β have?As the number of relevant independent variables in a regression increases, the R-squared of a regression Select one: a. exhibits greater heteroskedasticity b. increases c. decreases d. stays constantIf a regression equation contains an irrelevant variable, the parameter estimates will be Select one: a. Consistent and unbiased but inefficient b. Consistent and asymptotically efficient but biased c. Consistent, unbiased and efficient. d. Inconsistent
- True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.Which of the following is a consequence of severe multicollinearity in a regression model? A. High standard errors for the estimated coefficientsB. Lower standard errors for the estimated coefficientsC. The OLS estimator becomes biasedD. The dependent variable becomes constantAll the regression assumptions lie on the residuals, for both simple and multiple regression. True or False?
- 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 determinedWhich of the following are plausible approaches to dealing with a model that exhibits heteroscredasticity? i) Take logarithms of each of the variables ii) Use suitably modified standart errors iii) Use generalised least squares procedure iv) Add lagged values of the variables to the regression equation Answers: a- (i), (ii), (iii) and (iv) b- (ii) and (iv) c- (i) and (iii) d- (i), (ii) and (iii) What is the answer?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 model
- Quantile regression (QR) is different from OLS in that: a. QR estimates marginal effects at the mean values of the dependent variables. b. QR does not estimate marginal effects at the mean values of the dependent and independent variables. c. QR minimizes the sum of squared residuals to obtain the coefficient estimates. d. QR only uses the data below the quantile where the quantile regression is being estimated.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.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.