IGNOU MSTE 2 2026 - A firm wants to know whether there is any linear relationship between

Question

A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained:
$$\sum X = 265, \sum Y = 27.73, SS_X = 285.6, SS_Y = 6.978 \text{ and } SS_{XY} = 57.456.$ $
(a) Fit a regression line taking Y as the dependent variable and X as the independent variable.
(b) Test whether the sales have any effect on revenue at 5% level of significance.
(c) Comment on the goodness of fit of the regression line.

19 Jan 2026

Answer :

Word Count : 285

For the given data, the number of observations is (n = 10). The regression of (Y) on (X) is of the form [ Y - \bar{Y} = b_{YX}(X - \bar{X}) ] where [ b_{YX} = \frac{SS_{XY}}{SS_X}. ] First compute the means: [ \bar{X} = \frac{\sum X}{n} = \frac{265}{10} = 26.5, \quad \bar{Y} = \frac{\sum Y}{n} = \frac{27.73}{10} = 2.773. ] The regression coefficient

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