.,n, 1.4. Show that in a linear regression model yt- B1t2, t-1, the squaredmultiple correlation coefficient...
Question 4 Consider the linear regression model 1. For estimates βί, 「= 1,.. . , n, the residuals are given by Explain why. 2. Show the first order condition for 30 is Σηι ei = 0. 3. Show the first order conditions for B,... , Bk are respectively. (Hint: Consider your calculation from Question 1.)
Consider a population linear regression model: Yt=β0 + β1Xt + ut Calculate: 1. Variance 2. Covariance of ut and Xt 3. β0 4. β1
1. (20 points) Consider the linear regression model y = a + Bt + ut, ut id(0,%), (t = 1, ...,T). An estimator of B is b=1-1 YT- 41 (a) is estimator b consistent? (Hint: use Chebyshev's inequality) (b) If u i.i.d. N(0,1), what is the asymptotic distribution of b?
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
correlation and regression 210 Statistics EXTRA CREDIT Correlation and Regression Formulas written Assignment 1. Follow the instructions below to calculate the correlation coefficient and least squares regression line for the data set below. Z 22,- The sample means and sample standard deviations for the two variables are listed below: X = 4 x = 2 3 =5 Sy = 1 The linear correlation coefficient is = 52. Calculate this correlation coefficient using the steps below: (a) First, complete the columns...
This question asks you to compute the sample correlation coefficient (?xy ) and estimate the regression coefficients with ordinary least squares (OLS) “by hand” for the model (Yi = ?1 + ?2Xi +ui) using the data below, but without using R (except to get critical values or p‐values, and to check your work) y x 1 2 5 6 4 4 4 6 1 2 A. Compute and report the sample correlation coefficient B. Can you reject the null hypothesis...
Consider the simple linear regression model: Yi = Bo + Bilitei, i = 1,...,n. with the least squares estimates ỘT = (Bo ß1). We observe a new value of the predictor: x] = (1 xo). Show that the expression for the 100(1 - a)% prediction interval reduces to the following: . (xo – x2 Ēo + @130 Etap 11+ntan (x; – 7)2
Problem 1 Consider the simple linear regression model Ya-Rit Bix, + εί. Prove that when are the LS estimates the following holds: and βί im1 i-l
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose the following sample is observed. 6 X 2 10 8 4 Y 3 4 5 6 2 4.8 3.Y 4c (1) Find the OLS estimates for B, and B2. (2) Compute the estimate of Var(u). (3) What are the variances of the OLS estimates? (4) Compute the coefficient of determination. (5) Show the relationship between r2 and Dxy (6) Compute the correlation coefficient pxy...
What does the error term in the simple linear regression model account for? What are the parameters of the simple linear model When all the points fall on the regression line, what is the value of the correlation coefficient? Part of an Excel output relating 15 observations of X (independent variable) and Y (dependent variable) is shown below. Provide the values for a-e shown in the table below. (See section 15.5) Summary Output ANOVA df SS MS F Significance F...