Final answer:
If x increases by one unit in the simple linear regression model y = β0 + β1x + ε, y is expected to change by the coefficient β1, which is the slope of the line.
Step-by-step explanation:
The simple linear regression model y = β0 + β1x + ε implies that if x goes up by one unit, we expect y to change by the amount of the slope β1. This change is irrespective of the value of x, meaning it is constant for any value of x. The term β1 represents the slope and is a measure of how much y is expected to increase (or decrease if β1 is negative) when x increases by one unit. The variable ε represents the error term and is not relevant to the question of how y changes with respect to x. So the correct answer to the question is β1.
Graphically, if a line has a larger intercept, it shifts out or up from the old origin, maintaining its slope, while a line with a smaller intercept shifts in or down. Economists use linear models to solve models with algebra and answer questions like the impact of economic growth on unemployment. This involves algebraically solving the system of equations to find solutions to specific scenarios.