b) You are given the following modelμ = 2x + yv=x-yi) What is the standard deviation (₂)?ii) What is the covariance of u and v (0)?

Answered: b) You are given the following model…

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).
X= 80, Me = 70, Lower Quartile (Qı) = 20, Upper quartile (Q3) = 100 and S.D From the data given below, ascertain (1) Pearson's Coefficient of Skewness, and (11) Bowley's Coefficient of Skewness %3D %3D %3D
12
14. In a regression context, under what situation is the predicted value for Y equal to the mean of Y? a) when the correlation between Y and X is positive b) when the correlation between Y and X is negative c) when the correlation between Y and X is zero d) when we try to predict Y in the complete absence of X e) a and d f) c and d g) none of the above, the predicted value for Y is only equal to the mean when X is equal to 0
(b) For a given set of trivariate data, the following results were obtained: X = 53, Y = 28, 6 (Y on X) =- 1.5, d (X on Y)=- 0.2. Find : (i) The two regression equations. (ii) the coefficient of correlation. (iii) The most probable value of Y when X=60.
Q2: For the raw data shown in Table below: 1) Find out which of the x₁ or x₂ variables is better correlated to y. 2) Find out the linear regression lines: y₁ = f(x₁) and y2 = f(x₂) depending on the results of 1) above. X1 1 3 4 11 14 X2 1 2 3 12 15 y 1 2 4 9 65 87 99 4 5 сл 7 12 8
If the slope of a regression line (b1) is 1.5, then a) for every unit of change in x, there is a change of 1.5 units in y b) for every unit of change in y, there is a change of 1.5 in x. c) the score of each case is 1.5 times higher on yt han on x d)y causes X
R1
C Find the equation of the 3x-24 = CH normal line at the point (-1,-6)
E For the bivariate data at right, do the following. (a) Make a scatter plot and find the correlation coefficient. (b) Create a new variable U = VY. Make a scatter plot of X and U, and find the correlation coefficient of X with U. Also find the equation of the regression line of U upon X, and sketch the regression line in the scatter plot. (c) Use the equation of the regression line in part (b) to derive an equation relating Y and X, and sketch the graph of that equation in the original scatter plot. Y 7 16 10 25 149
A group of children were asked to draw a circle the size of a nicket, without having a nickel to see. In the data below, x= Incomes (in thousands of $) of the the family and y= the diameter of the circle drawn. Test for a significant correlation between income and drawn nickel size. Income (thousands of $) Coin size (mm) 33 25 20 23 36 16 47 22 22 34 14 27 23 20 45 27 24 39 23 91 22 42 12 84 18 46 18 45 22 90 13 54 22 45 18 90 16 54 19 You can copy the data into StatCrunch, Excel, or Google Sheets, by highlighting the data, right-clicking, and selecting Copy (or Ctrl • c), then open a StatCrunch, Excel, or Google Sheets spreadsheet, click on the first cell, and right-clicking and selecting Paste (or Ctri + v). Test the claim that there is significant correlation at the 0.02 significance level. Retain at least 3 decimals on all values. a) Identify the correct hypotheses. Họ:r = 0 HA:r +0 Ho:4 = 0

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b) You are given the following model μ=2x+y v=x-y i) What is the standard deviation (₂)? ii) What is the covariance of a and v(a)? - D