state the limitations of using a cubic function with inflection point to model the side of a hill. What assumptions have been made that may affect the reasonableness of your solutions?

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?

You are given information on the use of public transportation in the data set within the image. Number of weekly riders                                     y -variable Price per week (of using public transportation) x-variable Population of city                                                 x-variable Monthly income of riders                                     x variable         Average parking rates per month x-variable   (a) Run a regression of the Number of weekly riders on Price per week, Population of city, Monthly income of riders, Average parking rates per month. Please copy and paste your regression results and do not submit your EXCEL worksheet.   (b) If the average parking rates increase by $1, what will be the change in the number of weekly riders? Will this change be a statistically significant change? Please explain.   (c) If the price per week (of using public transportation) increases by $1, what will be the change in the number of weekly riders? Will this change be…

A lake has two species of fish: bass and catfish. The number of bass and catfish living in the lake, B and C respectively, depend on the temperature of the lake, T (in degrees Farenheit). The functions modeling this dependency are given below: B(T) = 8T2 + 976T – 28890 С(Т) 3D — 2T?+244T — 6893 What are the two temperatures at which the number of bass in the lake is the same as the number of catfish? Enter exact expressions or round your answers to the nearest thousandth. T : T

Explain why in every econometric model there must be an error term, explain its function.

1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3

18. A multiple regression model, K = a + bX + cY + dZ, is estimated regression software, which produces the following output: D. If X equals 50, Y equals 200, and Z equals 45, what value do you predict K will take?

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?

Which of the following statements is true under the Gauss-Markov assumptions? a. Among a certain class of estimators, OLS estimators are best linear unbiased but are asymptotically inefficient. b. Among a certain class of estimators, OLS estimators are biased but asymptotically efficient. c. Among a certain class of estimators, OLS estimators are best linear unbiased and asymptotically efficient. d. The LM test is independent of the Gauss-Markov assumptions. O a. a O b. b О с. с O d. d