Compute the coefficients of a Fisher discriminant to separate samples of data A and B given the means and covariance matrices v below. 3.2, -(0.0,1.4) -(0.0,0.9) μA = (1.0, 2.0), µB = (-1.0, 3.0), VA = UB
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- For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.A random variable X is normally distributed with a mean of 100 and a variance of 500, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to -0.5. Find the mean and variance of the random variable:W = 5X - 4Y3. Let X be the nxp data matrix, define the deviation vector as d; = (x1j-Tj, ..., Xnj T;)'. Let 0 be the angle between the jth and Ith deviation vectors. Calculate the lengths of ||d;|| and cos(0). Relate these quantities to the sample covariance and sample correlation.
- Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 0Are any of the variables significantly correlated? If so, which ones and in which direction (positive or negative)? Correlation matrix: Health Score Anxiety Score Anxiety 0.13994335 Score (0.5047) Stress Score 0.38584335 0.010340294 (0.0568) (0.9609)
- In a sample of size200,the correlation coefficient is 0.45. Is thecorrelation coefficient is significant under the population. α=0.05If X, Y and Z are uncorrelated and independent variables with the same variance o? and zero mean. find the correlation coefficient between (X +Y) and (Y +Z).Suppose that given a particular dataset of (x, y) pairs, the correlation coef- ficient (r) of the least-squares line is -.98. What conclusion can we draw from this 19. information? A. X and Y have a strong linear correlation B. X and Y have a moderate linear correlation C. X and Y have a weak linear correlation D. X and Y are not linearly correlated E. None of the above 20. Given the following summary data from a sample of size 9, what is the slope of the least-squares line for x and y? E; = 24 Σ-70.50 Σ- - 902.25 Ev = 11, 626.75 Yi = 312.5 %3D A. .089 В. 13.150 C. 13.052 D. 10.603 E. None of the above
- In the least-squares regression model, y; = B,x; + Bo + 8j, e, is a random error term with mean and standard deviation o. = ... In the least-squares regression model, y; = P1X; + Po + &j, &¡ is a random error term with mean V and standard deviation og =During the graphical analysis of the data below, two different curves were fitted to the data using the least squares method. The curves are as follows. Decide which curve is more suitable by calculating the correlation coefficients.