Final answer:
The fraction of variability in bean heights that can be explained by the linear model of bean height vs width can be determined using the coefficient of determination, also known as R-squared. It measures the proportion of the variability in the dependent variable that can be explained by the independent variable.
Step-by-step explanation:
The fraction of variability in bean heights that can be explained by the linear model of bean height vs width can be determined using the coefficient of determination, also known as R-squared. R-squared measures the proportion of the variability in the dependent variable (bean heights) that can be explained by the independent variable (bean width). It ranges from 0 to 1, with a higher value indicating a stronger relationship.
To calculate R-squared, you need the sum of squares total (SST), which represents the total variability in the dependent variable, and the sum of squares error (SSE), which represents the unexplained variability. The formula for R-squared is: R-squared = 1 - (SSE/SST)
Once you have calculated R-squared, you can interpret it as the proportion or percentage of the variability in bean heights that can be explained by the linear model of bean height vs width. For example, if R-squared is 0.8, it means that 80% of the variability in bean heights can be explained by the linear model.