Question

What is the primary purpose of a regression line?

a) To calculate derivatives
b) To model relationships between variables
c) To find local extrema
d) To solve linear equations

Answer 1

The primary purpose of a regression line is to model relationships between variables and analyze the relationship between an independent variable and a dependent variable.

Step-by-step explanation:

The primary purpose of a regression line is to model relationships between variables. It is used to analyze and predict the relationship between an independent variable and a dependent variable. The regression line provides an equation that represents the best-fit line for the data, allowing us to make predictions about the dependent variable based on the independent variable.

To understand the purpose of a regression line, let's go through the steps:

1. Decide which variable should be the independent variable and which should be the dependent variable. The independent variable is the one that is controlled or manipulated, while the dependent variable is the one that changes in response to the independent variable.
2. Draw a scatter plot of the data. This helps visualize the relationship between the variables.
3. Calculate the least-squares line. This line represents the best-fit line for the data and is obtained by minimizing the sum of squared errors (SSE).
4. Find the correlation coefficient. The correlation coefficient measures the strength and direction of the linear relationship between the variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship, +1 indicates a perfect positive relationship, and 0 indicates no linear relationship.