Calculate the coefficient of determination, 𝑅2, from raw data using technology, and interpret it to assess the strength of a linear association in terms of the explained variation.

A biologist collected data on plant stem height (in cm) and leaf area (in cm²) from 15 samples of a species. Using technology to fit a least-squares regression line, she obtained an $R^2$ value of $0.943$. What percentage of the variation in leaf area is explained by the linear relationship with stem height?

A researcher collected data on the number of study hours per week and the final examination scores (out of 100) for 12 students. Using technology to perform a linear regression analysis, the coefficient of determination was calculated as $R^2 = 0.8436$. (a) Calculate the percentage of the variation in examination scores that is explained by the linear relationship with study hours. (1 mark) (b) Interpret this result to describe the strength of the linear association between study hours and examination scores. (2 marks)

A researcher is investigating the relationship between weekly study hours and final exam scores for first-year university students. The data collected from eight students is shown in the table below. (a) Use technology to calculate the coefficient of determination, R², for the relationship between weekly study hours and exam scores. (1 mark) (b) State the percentage of variation in exam scores that is explained by the linear relationship with weekly study hours. (1 mark) (c) Interpret the R² value in context to assess the strength of the linear association. (2 marks)