A scientist studied the relationship between the number of ferns, x, per acre and the number of rabbits, y, per acre in a neighborhood. She modeled the relationship with a scatter plot and used the equation y=10+3x for the regression line. What is the meaning of the slope and the y-intercept of this regression line?
The slope of the regression line, in this case 3, represents the average increase in the number of rabbits per acre for each additional fern per acre. So for every additional fern that grows on the acre, the scientist would expect to see, on average, 3 more rabbits.
The y-intercept of the regression line, in this case 10, represents the expected number of rabbits per acre when there are no ferns present. This means that even if there are no ferns growing in the neighborhood, the scientist would still expect to see, on average, 10 rabbits per acre.