For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) =c,Find:а. Var(3X — 5Y).b. The correlation coefficient between X and Y, p.The range of values of c for which the assumptions of the problem are consistent.С.

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Answered: For random variables X and Y such that…

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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4. Consider the Normal regression problem: Y,- N(a + Br, o) where a, 3. are unknown. Recall the following: a = Y- 37 S = SY = En - F)(Y - Y). Show that S,y E,(r, - 2)Y- Show that Cov(Y, Y) = for all i. Use part a and b and linearity of Covariance to show that Cov(8, Y) = 0. Show that Var(3) = ) „how that Cov(a, B) = - (Hint: part a , b and d may be useful in this cauculation).
Q1. The values of X and Y are given in the following table. X0235 8. Y 157 11 | 17 = 18. Y = 41, xY 222, > x² = 102, > Yy² X = 485 a) Find the Coefficient of Correlation b) Find the Coefficient of Determination and Coefficient of Non-Determination? c) Calculate the line-of-best- t (linear regression line) Ý = a + bX, d) If x = 8, estimate the response y.
The table below summarizes x and y values. Find the sample correlation coefficient, rxy using the formula below or by using calculator regression between x and y? Is there a good linear relationship y 2.73 3.32 4.44 0.5 Ey.cx; – 3) 1 i=1 1/2 7.22 9.34 E0; – £ (x; – F)² 10 11.35 i=1 i=1 15 15.54
In a simple linear regression model, B1 has important relationships with a sample correlation coefficient r. Prove the following two identities. Tyn – 2 Syy SIT (2) se(3) (1) B
The linear correlation between an independent (x) and dependent (y) variable A. Is the foundation for simple (bivariate) regression B. Does not indicate a causal relationship, though one might exist C. Can be direct, inverse, or nonexistent D. Can be used to predict the value of y for any observed value of x E. All of the above F. None of the above
Commercial Movie Releases The yearly data have been published showing the number of releases for each of the commercial movie studios and the gross receipts for those studios thus far. The regression line equation is y′=+225.124+7.185x. The correlation coefficient is r=0.872. Compute the standard error of the estimate rounded to at least two decimal places, if appropriate. Assume α=0.05 No. of releases, x 10 8 270 35 12 306 361 22 Gross receipts, y (million $ ) 241 188 1962 334 154 1371 3844 1064 The standard error of the estimate should be calculated. s est = The standard error of the estimate should not be calculated.
Solve for the predicted values of y and the residuals for the following data. x 12 21 28 8 20 y 17 15 22 19 24 Do not round the intermediate values. (Round your answers to 3 decimal places.) x y Predicted (ŷ) Residuals (y-ŷ) 12 17 21 15 28 22 8 19 20 24
7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannel
45. Calculate the correlation coefficient from the following results : N- 10, Σ X= 350 Σ Υ- 310 Σ (X-35= 162, Σ (Y- 31)? = 222 E (X-35) (Y-31) = 92. erlw %3D %3D Also find the regression line of Y on X

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For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) %3D с, Find: а. Var(3X — 5Y). b. The correlation coefficient between X and Y, p. The range of values of c for which the assumptions of the problem are consistent. C.