Bivariate data – Further Maths Paper 2 Statistics

Candidates should be able to:

• understand the concept of least squares, regression lines and correlation in the context of a scatter diagram;
• calculate, both from simple raw data and from summarised data, the equations of regression lines and the product moment correlation coefficient, and appreciate the distinction between the regression line of $$y$$ on $$x$$ and that of $$x$$ on $$y$$;
• recall and use the facts that both regression lines pass through the mean centre ($$\bar{x}$$, $$\bar{y}$$) and that the product moment correlation coefficient r and the regression coefficients $$b_1$$, $$b_2$$ are related by $$r^2 = b_1 b_2$$;
• select and use, in the context of a problem, the appropriate regression line to estimate a value, and understand the uncertainties associated with such estimations;
• relate, in simple terms, the value of the product moment correlation coefficient to the appearance of the scatter diagram, with particular reference to the interpretation of cases where the value of the product moment correlation coefficient is close to $$+1$$, $$−1$$ or $$0$$;
• carry out a hypothesis test based on the product moment correlation coefficient.