6 observations on $(X, Y)$ yielded the following data: &n

Question

6 observations on $(X, Y)$ yielded the following data:

\sum X_i = 30, \sum Y_i = 180, \sum X_i Y_i = 1000,
\sum X_i^2 = 200, \sum Y_i^2 = 5642.

i) Determine the correlation coefficient between X and Y.
ii) Given X = 10, what will be the predicted value of Y?
iii) Given Y = 15, what will be the predicted value of X?

09 Jan 2026

Answer :

Word Count : 358

We are given 6 observations with the following sums: [ \sum X_i = 30, \quad \sum Y_i = 180, \quad \sum X_i Y_i = 1000, \quad \sum X_i^2 = 200, \quad \sum Y_i^2 = 5642 ] Number of observations: ( n = 6 ). Step 1: Compute the means of X and Y. [ \bar{X} = \frac{\sum X_i}{n} = __________ _______ ______ ______ __________ ____ ____.
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