Correlation, regression of y on x and Spearman's rank

Learning objectives

Draw a scatter diagram and describe the association between two variables by its direction, form and strength, and identify any outliers

Calculate Pearson's product-moment correlation coefficient r with technology, interpret its sign and its magnitude, and explain that r only measures linear association

Find the equation of the least squares regression line of y on x with technology, interpret the gradient as the change in y for a unit change in x and the intercept as the value of y when x is zero, and use the fact that the line passes through the mean point (x̄, ȳ) when drawing a line of best fit by eye

Use the regression line of y on x to predict a value of y, explaining why it should not be used to predict x from y and why extrapolation beyond the data range is unreliable

Calculate Spearman's rank correlation coefficient rs by ranking each variable, and explain that it detects monotonic rather than linear association and is less affected by outliers

Explain that a strong correlation does not establish a causal link, and suggest possible confounding variables in a given context