15. If x₁=Y1+ y2, X2 = y2 + Y3, x3 = y3+y₁, where y₁, y2 y3 are correlated variables each of which has zero mean and unit standard deviation, find the multiple correlation coefficient x₁ and the two variables X2, X2.
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Suppose that X and Y are unknowns with E(X) = 10, Var (X) = 4, E(Y)=12 and Var (Y) = 100. In addition, suppose that the correlation coefficient of X and Y is .6. Then what is the variance of X-Y?Suppose Y1, Y2 and 3Y are not correlated variables, however, have the same standard deviation. Show that correlation between Y1 + Y2 and Y2 + Y3 is equal to half. Whether correlation coefficient is zero or not
- 8/20 Compute the correlation coefficient and determine whether there is a linear relation between X and Y.Imagine a study where all our data (x, y) falls perfectly on a flat and straight horizontal line. If we calculated the correlation coefficient r for this data, what would it be? What would that mean for our hypotheses?Why does a correlation table have a diagonal line of 1s? 1 Because the sum of all correlation coefficients must equal one. 2 Because it’s the result of a dummy variable. 3 Because p-values cannot be greater than one. 4 None of these 5 Because it acts as a benchmark for all other correlation coefficients.