Final answer:
The statement that regression analysis finds the line of best fit and often involves multiple variables is true. Regression uses the least-squares method to minimize error and predict outcomes, with the significance of the relationship assessed by the correlation coefficient.
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 to examine the relationship between two or more variables. Its primary goal is to model the linear relationship between the independent variable(s) and the dependent variable. The regression line equation that we calculate from the sample data gives the best-fit line for our particular sample, and this line can be used to make predictions within the dataset.
When plotting a scatter plot and determining the line of best fit, residuals or errors are considered, which measure the distance between the actual and estimated values of the dependent variable. The line that minimizes the sum of the squared errors (SSE) is deemed the best-fit line, and this is typically achieved using the least-squares method. After this line is drawn, the correlation coefficient can be calculated, which assesses the strength and direction of the linear relationship between the variables.
It is important to examine the significance of the correlation coefficient and the scatter plot itself to evaluate whether the best-fit line calculated from the sample data appropriately represents the population. If the relationship between the variables is significant, one can confidently use the line of best fit to make predictions about the dependent variable when given new values of the independent variable(s). However, predictions should not be made for values outside the data set because the relationship could change beyond the range of the observed data.