Consider the following linear regressionYi = X;ß+ uj,where i = 1, ..., 6; x¡ = 3i; y = (1,2, 3, 4, 5, 6)'; and o? = 1.Find the OLS estimator of B.Moreover, find the unbiased estimator of o?.

Given the linear regression as yi=xiβ+ui where i=1,...,6 ; xi=3i ; y=1, 2, 3, 4, 5, 6' ; σε2=1.

Answered: Consider the following linear…

Consider the following linear regression Yi = x;ß+ u;, where i = 1, ., 6; x; = 3i; y = (1,2, 3, 4, 5, 6)'; = 1. Find the OLS estimator of ß. Moreover, find the unbiased estimator of o?.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

See similar textbooks

Related questions

Q: True or false? If the statement is false, use one or two sentences to justify your answer.

A: The negative correlation indicates that the relationship between x and y is inverse in nature and…

Q: Consider the following regression equation specied for 2-period panel data: where i = 1; 2; :::N…

A: Given β_1 is positive, but the correlation between Δx_i and Δu_i is negative, thenwhat is the bias…

Q: Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have…

A: Solution: Given information: n= 11 observation. k= 3 explanatory or predictor variables. Sum of…

Q: Consider the linear regression model Y; = Bo + B, X; +U; for each i = 1,..., n with n = 1,000. X;…

Q: Suppose you estimated the multiple linear regression of y on x1 and x2, and found that the estimated…

A: Introduction: There are two models considered here: Model 1: Multiple linear regression model of y…

Q: Consider the following simple regression model y = B0 + B1x1 + u and z is an instrument for x.…

A: Given Information: Consider the simple regression model: y=β0+β1x1+u (z is an instrument…

Q: Consider the following regression equation: Y,= Po+PX;+Hi where X, Y. Bo. B1, and , denote the…

A: Finding the heteroskedastic-robust estimator of the variance β^1

Q: Consider the following regression equation: Y = Bo +P,X;+H. where X,, Y. Po B, and u, denote the…

A: Given : Regression equation : yi = β0 + β1 xi + μi

Q: Consider a simple linear regression model Yi = Bo + B1x; + Ei, i = 1, 2,3 with x; = i/3 for i = 1,2,…

A: Given a simple linear regression model yi=β0+β1xi+εi , i=1, 2, 3 with xi=i3

Q: 6. Compute the two regression equations on the basis of the following information: Mean 40 45…

A: Introduction - Regression equation y=a+bxb=r.sysxa=y-bxwhere , y=Mean of y values x=mean of x -…

Q: In a simple linear regression, show that the OLS regression line always passes through the mean…

A: Let, yi=a+bxi+ui be the population regression line and yi=a^+b^xi+ei^ be the sample regression…

Q: Suppose that a multiple linear regression model is fitted for the prediction of average live weight…

A: In this case, the utility of fitted model for predicting Y can be determined by testing the overall…

Q: Define the ADL and GLS Estimators of Regression.

Q: For variables x1, x2, x3, and y satisfying the assumptions for multiple linear regression…

Q: Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we…

A: Given that one of the data should be ( x1=10, y1=30) which is incorrectly recorded as (x1=7,y1=34).…

Q: Consider a special linear regression model in which each observation has its own slope coeficient:…

A: Given the special linear regression model as yi=xiβi+εi , i=1, . . . , n

Q: Consider a simple linear regression model Y; = Bx; + €i, where e; are independently and identically…

A: Step 1: Consider the simple linear modelYi=β xi+εi where εi are iid with mean 0 and variance σ2. We…

Q: Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have…

A: SOLUTION:- Given SSR=85000 SSE=15000

Q: Show that the correlation coefficient between the residuals X2.13 is equal and opposite to that…

Q: In a study of the relationship between marble ownership and household income, the Grinch interviewed…

A: The regression is given by, y= a + bx Here, y : weight of marble owned by household (lbs) x :…

Q: Use the following model generated from backwards multiple linear regression to estimate VOzma (ml-kg…

Q: Find out the regression coeticients of Y on X and X on Y from the following data: ΣΧ= 50 , X= 5, Σ Υ…

Q: I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive…

A: Given: The linear regression model, y=b0+b1x1+b2x2+e

Q: Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n…

A: Regression analysis

Q: The following table gives the marks obtained by 10 students in POLI 344 (X) together with the marks…

A: Given: n = 11 Formula Used: Regression equation of Y on X: Y = a + bX Slope b = n∑XY-∑X∑Yn∑X2-∑X2…

Q: In order to test for the significance of a regression model involving 5 independent variables and…

A: Given information No of independent variables(k) =5 No of observations(n) =123

Q: In the following model, "employed" is a dummy indicating a person is employed: donation = B + B edu…

A: Dummy variables are those variables that can take the values such as 0 and 1. Dummy variable can be…

Q: Suppose the following data were collected from a sample of 15 CEOS relating annual salary to years…

A: The independent variables are experience, service and industrial. The dependent variable is salary.…

Q: Suppose the following data were collected from a sample of 15 CEOS relating annual salary to years…

A: First we need to test whether there is enough evidence to support the claim that on average, CEOs in…

Q: 6. (a) Show that in the simple linear regression setting, the usual F test statistic of Họ: B1 = 0…

A: Given the F test statistic of H0 : β1=0 as F=R2n-21-R2

Q: Consider the following diagnostics table from a multiple linear regression with 2 covariates: ID…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 25/ A: Use Linear Regression to fit the following experimental data

A: Given, X 0 3 2 3 1 6 5 Y 5 1 2 10 9 8 10

Q: In the following model, "employed" is a dummy indicating a person is employed: donation = B + B edu…

A: Regression is used to predict the value of dependent variable by using one or more independent…

Q: Calculate the correlation coefficient from the following results : N=10,sigmax= 350,Sigma Y= 310…

Q: In order to test for the significance of a regression model involving 10 independent variables and…

A: Introduction: The multiple linear regression equation of the response variable, y, on k predictor…

Q: An econometrician suspects that the residuals of her model might be autocorrelated. Explain the…

A: The Durbin Watson Test is a measure of autocorrelation in residuals from regression analysis.…

Q: Find out the regression coefficients of Y on X and X on Y from the following data: ΣΧ= 50, X= 5 , Σ…

A: It is given that variance of X is 4 and the variance of Y is 9.

Q: obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and are…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Consider the simple linear regression model =a+Bx+E for i = 1,2,...,n. The variances of two…

A: we wants to estimate the variance of the regression estimators of a regression line: yi=α +β *xi +∈i…

Q: Consider the following population linear regression model of individual food expenditure: Y = 50 +…

Q: If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9.…

A: It is an application of statistics . It is highly useful in correlation as well as regression…

Q: The coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the…

A: Time series data provide the possibility to estimate the time path of the effect on Y of a change in…

Q: Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the…

A: Given, the correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. We need to calculate the…

Q: Let Y, be the predicted value of Y in this regression. Let 6 be the residual of a regression of Xi…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 2. The coefficient of determination of a simple linear regression model based on 10 sample points…

A: Introduction: Denote SST as the total sum of squares of a regression model, SSR as the regression…

Q: Consider the following regression model: Y; = Bo + B1X1i + B2X2¡ + B3X3¡ + B4X4¡ + Ui We want to…

A: From the given information, The regression model is, And H0:β3+β4=0 vs H1:β3+β4≠0 The regression…

Q: When considering the regression model y,-Po+P,,+,+w,+", Which of the above will not be evidence of…

A: The Heteroscedasticity can also be identified by constructing residual plots between the explanatory…

Question

Consider the following linear regression
Yi = X;ß+ uj,
where i = 1, ..., 6; x¡ = 3i; y = (1,2, 3, 4, 5, 6)'; and o? = 1.
Find the OLS estimator of B.
Moreover, find the unbiased estimator of o?.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.
For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.