What does the slope represent in simple linear regression y = β0 + β1 x?

What does the slope represent in simple linear regression y = β0 + β1 x?

• A. The intercept value of y when x = 0.
• B. The proportion of variance explained.
• C. The average change in y for a one-unit increase in x.
• D. The strength of the correlation.

Answer: (C)

In simple linear regression, the slope tells how much y is expected to change as x changes. Specifically, for each one-unit increase in x, the predicted value of y changes by β1 units. This is the average rate of change of y with respect to x along the fitted line (the derivative dy/dx for a linear model). The intercept is the value of y when x is zero, not the slope. The proportion of variance explained (R^2) describes how well the line fits the data, not how y changes per unit of x. The strength of the correlation describes how tightly x and y follow a linear pattern, but not the amount of change per unit of x. So the slope embodies the average change in y for a one-unit increase in x.

In simple linear regression, the slope tells how much y is expected to change as x changes. Specifically, for each one-unit increase in x, the predicted value of y changes by β1 units. This is the average rate of change of y with respect to x along the fitted line (the derivative dy/dx for a linear model). The intercept is the value of y when x is zero, not the slope. The proportion of variance explained (R^2) describes how well the line fits the data, not how y changes per unit of x. The strength of the correlation describes how tightly x and y follow a linear pattern, but not the amount of change per unit of x. So the slope embodies the average change in y for a one-unit increase in x.