Use the correlation coefficient, 𝑟, to determine the coefficient of determination, 𝑅2, and vice versa.

A dataset has a correlation coefficient of $r = -0.85$. Which option shows the coefficient of determination?

A scatter plot of retail store sales against floor area shows a correlation coefficient of $r = 0.84$. Which statement correctly describes the relationship between these variables?

A marine biologist studies the relationship between ocean depth (metres) and water temperature (°C) at different locations along the continental shelf. The table shows measurements taken at eight locations. The coefficient of determination for the least-squares regression line modelling temperature as a function of depth is \(R^2 = 0.7396\). **(a)** Calculate the correlation coefficient, \(r\), for the data. **(2 marks)** **(b)** A second study examines the relationship between salinity (parts per thousand) and dissolved oxygen (mg/L) at coastal monitoring stations. For this second data set, the correlation coefficient is \(r = -0.68\). Determine the coefficient of determination, \(R^2\), for the salinity and dissolved oxygen data and interpret what this value means in the context of the study. **(3 marks)**

A linear regression analysis examines the relationship between monthly advertising expenditure (in dollars) and monthly sales revenue (in dollars) for a retail business. (a) The correlation coefficient between advertising expenditure and sales revenue is $r = 0.92$. Calculate the coefficient of determination, $R^2$, correct to 4 decimal places. [1 mark] (b) For a different product line, the coefficient of determination is $R^2 = 0.7225$. Use this to determine the possible values of the correlation coefficient $r$, correct to 4 decimal places. [1 mark] (c) Explain what the $R^2$ value from part (b) tells us about the relationship between advertising expenditure and sales revenue for this product line. [1 mark]