Final answer:
The correct model relating x2 to x1 in a simple linear regression is x2 = b0 + b1x1 + e. It involves estimating the relationship between the independent variable (x1) and the dependent variable (x2), represented by a line of best fit with an error term (e).
Step-by-step explanation:
The question asks about fitting a simple linear regression model, where x2 is the response variable and x1 is the independent variable. The correct form for the simple linear regression model is option b) x2 = b0 + b1x1 + e, where b0 is the y-intercept, b1 is the slope of the regression line, and e represents the error term or residual of the regression. In this model, x1 is the independent variable which we can use to predict the outcome of x2, the dependent or response variable.
Here are the key concepts to understand the process of regression:
- The independent variable is the variable that we believe has influence on the dependent variable; it is the predictor.
- The dependent variable is the variable that we are trying to predict; it is the outcome.
- A scatter plot is a graph used to visually represent the relationship between the two variables.
- The line of best fit, or least-squares regression line, is the straight line that best represents the data on a scatter plot.
- The slope (b1) indicates the change in the dependent variable for each unit increase in the independent variable.
- The y-intercept (b0) is the value of the dependent variable when the independent variable is zero.
- The error term (e) represents the difference between the observed value and the value predicted by the line of best fit.
- The correlation coefficient measures the strength and direction of the linear relationship between the two variables.
By analyzing data and using statistical tools such as linear regression, we can find the coefficients b0 and b1 to develop a predictive model that can be used for estimating the value of the dependent variable based on the value of the independent variable.