Final answer:
The regression values for the equation y = 9 + 3x are found by substituting the given x-values (1, 2, 3) into the equation: for x=1, y=12; for x=2, y=15; and for x=3, y=18. These values represent the dependent variable's response as the independent variable changes.
Step-by-step explanation:
The question refers to finding regression values in a linear equation, specifically y = 9 + 3x. In mathematics, particularly in algebra, linear equations like this one are fundamental in understanding relationships between two variables. In such equations, 'x' is known as the independent variable, and 'y' is the dependent variable, meaning that the value of 'y' depends on the value of 'x'. To find the regression values, we simply substitute the given x-values into the equation and solve for y.
- For x = 1: y = 9 + 3(1) = 9 + 3 = 12
- For x = 2: y = 9 + 3(2) = 9 + 6 = 15
- For x = 3: y = 9 + 3(3) = 9 + 9 = 18
Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. In this case, we are examining a simple linear relationship, where the output or regression values are obtained by plugging different x-values into the equation and then calculating the corresponding y-values, which would be plotted on a graph to represent the linear relationship.