IGNOU MTE 11 2026 - 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} = \frac{30}{6} = 5 ] [ \bar{Y} = \frac{\sum Y_i}{n} = \frac{180}{6} = 30 ] Step 2: Compute the correlation coefficient ( r ). The formula: [ r = \frac{n\sum X_iY_i - (\sum X_i)(\sum Y_i)}{\sqrt{\left[n\sum X_i^2 - (\sum X_i)^2\right]\left[n\sum Y_i^2 - (\sum Y_i)^2\right]}} ] Compute numerator: [ n\sum X_iY_i - (\sum X_i)(\sum Y_i) = 6(1000) - (30)(180) = 6000 -

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