QuestionIn the PRF represented in the equation (1), assumethe error termu¡ ~ i.i.d N(0,♂²), prove the OLS estimates ₁ is an unbiased estimate of b₁ .Suppose the PRF of two-variable regression is represented in the equation (1)Y₁ = b +b₁X¡ +u;, u¡ ~i.i.d N(0,0²)(1)We use Ordinary Least Square (OLS) method to estimate the coefficients in (1),

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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18 - Regresyon modelini bulunuz. Find the regression model.X Y 10 23 13 27 14 30 A) y=-3,16+0,58xB) y= 6,27+1,65xC) y=2,42+8,43xD) y=1,65+6,27xE) y=9,23+5,55x
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^ =?
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?
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 ____%.
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).
True or False, explain. Suppose two variables are related by the following formula: Z = 57X +3. The t-statistic on the null hypothesis that the slope coefficient is equal to zero will be the same in a regression of Y on X as in a regression of Y on Z.
Use the regression identity for multiple linear regression to show that R2 =1- SSE/SST. a. Explain why this formula shows that the coefficient of multiple determination can also be interpreted as the percentage reduction in the total squared error obtained by using the regression equation instead of the mean,y~, to predict the observed values of the response variable. b. Referring to , what percentage reduction in the total squared error is obtained by using the regression equation instead of the mean of the observed prices to predict the observed prices? c. Referring to , what percentage reduction in the total squared error is obtained by using the regression equation instead of the mean of the observed graduation rates to predict the observed graduation rates?
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.
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. Interpret the slope.
Consider a simple linear regression model with one predictor variable X and one response variable Y. The regression equation is given by Y = β0 + β1X, where β0 and β1 are the intercept and slope coefficients, respectively. The sample size is n = 100 and the coefficient of determination (R^2) for the model is 0.25. What can we conclude about the strength of the relationship between X and Y?
An agronomist is studying fertilization for potato farming. He compares the number of tones of potatoes produced per hectare (the yield) over several parcels of land. Different levels of phosphorus fertilizer are applied to each parcel of land. The results from his experiments are represented in the following scatter plot: The agronomist determined that the equation of a regression line that passes through points (0, 23) and (190, 37) corresponds to y = 0.07x + 23. If the agronomist wants to produce approximately 60 tonnes of potatoes per hectare, what quantity of phosphorus fertilizer (kg/ha) should he use. Describe the reliability of your answer with mathematical arguments.
(Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y . Suppose that X1 and X2 are uncorrelated. You estimate β1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.

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