The correct answer is $\boxed{\text{C}}$.
The slope coefficient is a measure of the relationship between two variables. In this case, the two variables are costs and machine hours. The slope coefficient tells us how much costs change for every unit change in machine hours.
To calculate the slope coefficient, we divide the difference in costs by the difference in machine hours. In this case, the difference in costs is $7000 and the difference in machine hours is $18000. Therefore, the slope coefficient is $7000 \div 18000 = 0.2571$.
Option A is incorrect because it is the product of the slope coefficient and the y-intercept. The y-intercept is the value of the dependent variable when the independent variable is zero. In this case, the y-intercept is not given.
Option B is incorrect because it is the square of the slope coefficient. The square of the slope coefficient is the variance of the dependent variable around the regression line. In this case, the variance of the dependent variable is not given.
Option D is incorrect because it is the sum of the slope coefficient and the y-intercept. The sum of the slope coefficient and the y-intercept is the value of the dependent variable when the independent variable is one. In this case, the value of the dependent variable when the independent variable is one is not given.