Chapter: Linear Regression· Mathematics & Statistics (Commerce) Part 2

For a bivariate data, \(\bar{x} = 53\), \(\bar{y} = 28\), \(b_{yx} = -1.2\), \(b_{xy} = -0.3\). Find : (a) Correlation coefficient between \(x\) and \(y\). (b) Estimate \(y\) for \(x = 50\).

Q.6 (A)(i) For a bivariate data, \(\bar{x} = 53\), \(\bar{y} = 28\), \(b_{yx} = -1.2\), \(b_{xy} = -0.3\). Find : (a) Correlation coefficient between \(x\) and \(y\). (b) Estimate \(y\) for \(x = 50\).

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Answer: (a) \(r = -0.6\) (b) \(y = 31.6\)

(a) \(r^2 = b_{yx} \cdot b_{xy} = (-1.2)(-0.3) = 0.36\), so \(r = \pm 0.6\). Since both regression coefficients are negative, \(r\) is negative: \(r = -0.6\).

(b) Regression equation of \(y\) on \(x\): \(y - \bar{y} = b_{yx}(x - \bar{x})\), i.e. \(y - 28 = -1.2(x - 53)\).

For \(x = 50\): \(y - 28 = -1.2(50 - 53) = 3.6\), so \(y = 31.6\).

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For a bivariate data, \(\bar{x} = 53\), \(\bar{y} = 28\), \(b_{yx} = -1.2\), \(b_{xy} = -0.3\). Find : (a) Correlation coefficient between \(x\) and \(y\). (b) Estimate \(y\) for \(x = 50\).

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