Final answer:
The statement is true; regression analysis does determine the line of best fit and can involve multiple variables. It includes the creation of a regression line equation using the least-squares method to make predictions and analyze the relationship between variables.
Step-by-step explanation:
The statement that regression analysis determines the line of best fit and often involves multiple variables is True. Regression analysis is a statistical method used for estimating the relationships among variables. It entails finding the equation of a regression line, often called the line of best fit, that most closely approximates the real data points in a scatter plot.
In linear regression, the simplest form involves one independent variable (x) and one dependent variable (y). The independent variable is the one you think might influence the other variable, like the length of a pinky finger in the given example. The dependent variable, such as a person's height, is what you aim to predict based on the value of the independent variable.
When a regression line is calculated using the least-squares method, it minimizes the sum of the squared differences (residuals or errors) between the actual data points and the predicted points on the line, finding the best fit for the sample data. With multiple regression analysis, more than one independent variable is used to predict the dependent variable. The concept of correlation is also essential in regression analysis; it measures the strength and direction of a relationship between two variables.
Correlation coefficients can be positive, indicating that as one variable increases, the other also increases, or negative, meaning that as one variable increases, the other decreases. The stronger the correlation, the more suitable the data is for linear regression analysis. Finally, regression lines can be used for prediction within the data set but should be applied cautiously when predicting outside of the data range.