Final answer:
A linear regression model with one predictor variable is known as a simple linear regression model. It fits a straight line to data using the equation y = a + bx where b is the slope and a is the y-intercept. This method is used to examine the relationship between two variables and to make predictions.
Step-by-step explanation:
If a linear regression model uses only one predictor variable, the model is referred to as a simple linear regression model. Simple linear regression is the process of fitting a straight line y = a + bx to a set of data points, where y is the dependent variable and x is the independent variable.
The equation y = a + bx includes the slope (b), which represents the rate at which y changes for a unit change in x, and the y-intercept (a), which is the value of y when x is zero. The process of finding the best-fitting line through the data points is known as the least-squares method.
Simple linear regression is often used to understand the relationship between two variables and can be a powerful tool in prediction. For example, if a student wanted to predict their final exam score based on their third exam score, and if the data shows a linear trend, simple linear regression could provide a model for making such predictions. The relationship between these two exam scores would be represented graphically as a straight line on a scatter plot, and the linear regression model would quantify the strength and direction of the association.