IGNOU BMTC 101 2026 - 6 observations on (X, Y) yielded the following data:

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.$

$\quad$ 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 : 377

First, note the given data: [ n = 6, \quad \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 ] Step i: Correlation coefficient (r) The formula for (r) is: [ r = \frac{n \sum X_i Y_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)}} ] Substitute the values: [ r = \frac{6(1000) - (30)(180)}{\sqrt{(6(200) - 30^2)(6(5642) - 180^2)}} ] Compute step by step: [ 6 \cdot 1000 = 6000, \quad 30 \cdot 180 = 5400 ] [ \text{Numerator} = 6000 - 5400

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