Show that the unbiased estimate of the model parameters are given by
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- propose a model that fulfill all five assumptions of the disturbance terms in classical linear regressionThe coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the dynamic causal effects when the time path of X is determined randomly and independently of other factors that influence Y. Explain How?The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.
- Use the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).The least-squares regression equation is y=728.0x+14,705 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8165. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is ___%, on average. For a median income of $0, the percent of adults with a bachelor's degree is ____%.Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE. Y X1 X2 1 40 25 2 45 20 1 38 30 3 50 30 2 48 28 3 55 30 3 53 34 4 55 36 4 58 32 3 40 34 5 55 38 3 48 28 3 45 30 2 55 36 4 60 34 5 60 38 5 60 42 5 65 38 4 50 34 3 58 38 Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.
- Find the least-squares regression line y^ =b0+b1x through the points (−2,0),(2,6),(5,14),(8,20),(10,26) and then use it to find point estimates y^ corresponding to x=1 and x=8. For x=1, y^ =? For x=8, y^ =?Find the least linear regression of (1, 0), (3, 3), and (5, 6)The annual energy consumption in billions of Btu for both natural gas and coal is shown for a random selection of states. Gas 223 474 377 289 747 146 Coal 478 631 413 356 736 474 If 500 billion Btu of natural gas is used then what is the projected amount of coal that is usedThe projected amount of coal that is used is billion Btu. (Use your regression equation with the rounded values for m and b to find your answer to this question. Round your answer to THREE decimal places, add extra zeros at the end, if needed) (Round answer to 3 decimal places, for example, XXX.XXX)
- How can we make predictions using a fitted model in R?Consider the fitted values from a simple linear regression model with intercept: yˆ = 5 + 6x. Assume that the total number of observations is n = 302. In addition, the R-squared of the regression is R2 = 0.6 and Pn i=1(xi − x¯) 2 = 15, where ¯x is the sample mean of x. Under the classical Gauss-Markov assumptions standard error of the estimated slope coefficient = 0.0365 value of the t-statistic for the null hypothesis H0 : the slope coefficient is equal to 0 versus H1 : the slope coefficient is different from 0 = 164.3836 What is the value of the F-statistic for the null hypothesis H0 : the slope coefficient is equal to 0 versus H1 : the slope coefficient is different from 0? Do the p-values of the t- and F-tests differ from each other? Justify your answer.justify the reasons for the in1.Econometrics deals with the measurement of economic relationships which are stochastic or random. The simplest form of economic relationships between two variables X and Y can be represented by: ; where are regression parameters and the stochastic disturbance term Justify the reasons for the insertion of U-term in the modelsertion of of u (error term) in the model Y=a+bX+u?