Given the model asobservations:What is the test statistic resulting from a test of the null hypothesis that the true value of the interceptcoefficient is zero?0.3 0.2 -0.1)(X'X)¹ = 0.2 0.6 -0.3-0.1 -0.3 0.4-0.5](X'y)= 0.40.2ū'ū = 0.6-1.1-0.09y₁ =B₁₂+ B₂x²₂, +B₂x₁₂ +14. Consider the following matrix estimated using 30 monthly0.60.3

The multiple linear regression model is given as:Sample size: and

Answered: Given the model as X=₁+₂+³+¹4. Consider…

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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Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1
Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
3. [3] Consider a simple linear regression model for (y, X), Yi = Bo + xiß1+ €;, where the e;'s are iid N(0, o²). Show that T2 = F, where T = VMSres/Saa and MSR MSres are used to test the hypothesis Ho : B1 = 0 (in simple and multip
After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS;) on a cow's body led to a different level of milk production (MP;). The researchers estimate the OLS regression: where WS, is a binary variable of the form: WS₁ = MP = 5.36 +0.26 x WS₁, (2.23) (0.06) 1, if the th cow has white spots 0, if the th cow doesn't have white spots The 95% confidence interval for the coefficient ₁ is (₁). (Round your answers to four decimal places.) Based on this interval, we will the hypothesis P₁ = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? O A. The coefficient is the sum of the conditional expectation of the presence of white spots on a cow with respect to the average milk production. OB. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white…
Suppose I estimate the following regression models with BP test p-values: == Y₁ =α0+α1Xi+ei Y₁ = ßo + B₁Xi + ß2X ² + vi pval = 0.76 p val = 0.056 pval = 0.00013 Y₁ = 00 + 01Xi + 02X² +03X3 + Zi At the 5% level, which functional form(s) seem(s) appropriate to describe the relationship between Yi and Xi. (a) Form (1) only (b) Form (3) only (c) Form (1) and (2) only (d) Form (1) and (3) only (e) Form (1), (2) and (3) (1)
Consider the following simple linear regression model, Y; = Po + B₁X₁ + εi, for i=1,2,...,n, where &'s are all independent and normally distributed with E(₁) = 0, and Var(₁) = 0². i) Check whether a statistic Y = Y + B₁ (X₁-X) is an unbiased estimator of the mean of the response variable E(Y) or not. Justify your conclusion.
2
6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)

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