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(Solved): The equation of the estimated least squares regression line of \( y \) on \( x \) for a set of biv ...



The equation of the estimated least squares regression line of \( y \) on \( x \) for a set of bivariate data is \( y=a_{1}+b

The equation of the estimated least squares regression line of \( y \) on \( x \) for a set of bivariate data is \( y=a_{1}+b_{1} x \) and the corresponding equation of \( x \) on \( y \) is \( x=a_{2}+b_{2} y \), where \( b_{1} \) and \( b_{2} \) are both positive. Systolic pressure is the blood pressure exerted by the heart when it is contracting and diastolic pressure is the blood pressure exerted by the heart when it is dilating. Table Q3c below shows the systolic and the diastolic pressure, in suitable units, of a patient taken at two-hourly intervals during a day. Table Q3c (i) Calculate the equation of the estimated least mean squares regression line of \( y \) on \( x \), giving the values of \( a_{1} \) and \( b_{1} \) correct to 3 significant figures. [4 marks] (ii) Calculate the product moment correlation coefficient \( \rho_{x y} \), correct to 3 decimal places, and state what it indicates about the relation between \( x \) and \( y \) over the data range. [2 marks] (iii) Write down an equation relating \( \rho_{x y}, b_{1} \) and \( b_{2} \), and hence deduce the least mean square regression line of \( x \) on \( y \). [2 marks]


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