Final answer:
Linear regression is recommended as a starting point in modeling due to its simplicity in establishing a linear relationship and its capability to predict outcomes using the line of best fit calculated through methods like the least squares method.
Step-by-step explanation:
One reason the textbook lists for why a linear regression is a good starting point in a modeling task is its simplicity in representing a linear relationship. When there is a significant linear relationship between two variables (x and y), linear regression can be used to predict the value of y for values of x that are within the observed data range. Linear regression utilizes a method, often the least squares method, to calculate the line of best fit with minimized residuals (the sum of squared errors), resulting in a model that can effectively estimate or predict outcomes within the scope of the data provided.
Understanding the significance of the correlation coefficient (r) is also essential in linear regression. If r is significant and the scatter plot displays a linear trend, we can confidently use the regression line as a model for the linear relationship in the population that our sample data represent.