Given two variables in the data matrix X (say the j1th and j2th variables). Show that their sample correlation will not change by standardization.
Given two variables in the data matrix X (say the j1th and j2th variables). Show that...
of two random variables, say X and Y. Suppose X is the head circumference of a person, and Y is the person's IQ score. If the correlation coefficient is found to be 0.7943, please interpret this with a brief statement. Use your own words!
Given a data matrix X as in Question 2, Assume the means of the p variables are zero. Let S = 1X,X be the sample covariance matrix. Let λι > λ2 > . . . > λ, be the ordered eigenvalues of S. Let el, . . . , ep be their corresponding orthogonal eigenvectors with unit length. In multivariate analysis, we usually want to use the first few eigenvalues and eigenvectors to represent the original data, as a tool...
Problem 3: Find a two-feature, five-example data matrix X E RX2 such that the two features have the correlation coefficient listed below. In each case, show your answer is correct, and plot the data in two-dimensional space. 5× (a) +1 (b) -1
show work please 56. Five observations taken for two variables follow. x 6 11 15 21 27 y, 6 9 6 17 12 a. Develop a scatter diagram for these data. b. What does the scatter diagram indicate about a relationship between x and y? c. Compute and interpret the sample covariance. d. Compute and interpret the sample correlation coefficient
Consider the following sample data for two variables. IC x 4 2 2 16 y 9 10 16 5 311 a. Calculate the sample covariance b. Calculate the sample correlation coefficient. c. Describe the relationship between x and y ell 1( a. S xy Round to two decimal places as needed) hi
2. The following sample of observations are given for two variables 12 6 20 3 21 1 19 2 18 3 You are told that the mean for x is 18, the standard deviation for x is 3.535534, and the mean for v is 3. a) Find the standard deviation for y b) Compute and the sample covariance for the above data c) Compute and interpret sign and the size of the sample correlation coefficient
Let x1, x2 denote the variables for the two-dimensional data summarized by the covariance matrix, the eigenvalues, and the unit eigenvectors shown below. Find a new variable y, of the form y 1 +ewh2-1, such that y, has maximum possible variance over the given data. How much of the variance in the data is explained by y,? 74.968-14.032. λι 78.245, 0.23 -0.97 u,-| and λ,-14.891, u,- 0.23 14.032 18.168 -0.97 Let x1, x2 denote the variables for the two-dimensional data...
Discuss two data characteristics that could invalidate the use of linear correlation and regression to show the relationship between two ratio scale variables.
show work Show Work Question Help Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) x 10 8 13 19 T 11 T 14 16 14 | y 7.46 6.77 12.74 7.12 7.81 8 .84 6.09 5.39 12 8.15 7 6.42 5 5.73 = Click here to view a table of critical values for the correlation coefficient a. Construct a scatterplot. Choose the correct graph below. OA OB. 638 12 16 06 12...
Given are five observations for two variables, x and y. xi 4 8 14 16 18 yi 58 52 45 24 11 The estimated regression equation for these data is y= 75.06 - 3.09x. A. Compute SSE, SST, and SSR using the following equations (to 2 decimal). B.Compute the coefficient of determination r2 (to 3 decimals). The least squares line provided an (good/bad) fit; ---------% of the variability in y has been explained by the estimated regression equation (to 1...