Bivariate Data
Learning Objectives:
• 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 and that the product
moment correlation coefficient r and the regression
coefficients b1, b2 are related by r ^2 = b1×b2;
• 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.
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