If \( \text{Var}(X_1) = 2 \), \( \text{Var}(X_2) = 4 \), \( \text{Var}(X_3) = 3 \), \( \text{Cov}(X_1, X_2) = 1 \), \( \text{Cov}(X_1, X_3) = -2 \), and \( X_2 \) and \( X_3 \) are independent, find the mean and variance of \( Y = X_1 - 2X_2 + 3X_3 \).

Answered: If Var(X1) = 2, Var(X2) = 4, Var(X3) =…

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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A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…
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Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin; - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team==== "Brooklyn Nets" Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1 80 Coef. Std. Err. MS 81 206.320988 8.439024 3.049595 -5.219512 2.156389 1459.95122 190.65061 t Number of obs F (1, 80) Prob > F R-squared. Adj R-squared = Root MSE P>|t| 2.77 0.007 -2.42 0.018 82 7.66 0.0070 0.0874 0.0760 13.808 [95% Conf. Interval]…
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If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are independent, find the mean and variance of Y = X1 – 2X2 +3X3.