In the regression equation y = b x + a, what does the parameter a represent?

In the regression equation y = b x + a, what does the parameter a represent?

• A. Intercept
• B. Slope
• C. Error variance
• D. Correlation

Answer: (A)

The parameter a is the intercept (the constant term) in the regression line. It represents the predicted value of y when x is zero, and it’s where the line crosses the y-axis. The slope, b, shows how much y changes for each unit increase in x. The remaining options describe aspects not encoded as a coefficient of the line: the error variance relates to how spread out the observed values are around the line, and the correlation measures the strength of the linear relationship between x and y, not a parameter in the regression equation.

The parameter a is the intercept (the constant term) in the regression line. It represents the predicted value of y when x is zero, and it’s where the line crosses the y-axis. The slope, b, shows how much y changes for each unit increase in x. The remaining options describe aspects not encoded as a coefficient of the line: the error variance relates to how spread out the observed values are around the line, and the correlation measures the strength of the linear relationship between x and y, not a parameter in the regression equation.