the graph would slope downward, as the blue line does in panel (a). Of course, b could equal zero. If it does, a one-unit increase in X causes no change in Y so the graph of the line is flat, like the black line in panel (a).
The value of a has no effect on the slope of the graph. Instead, different values of a determine the graph's position. When a is a positive number, the graph will intercept the vertical Y-axis above the origin, as the red line does in panel (b) of Figure A.3. When a is negative, however, the graph will intercept the Y-axis below the origin, like the blue line in panel (b). When a is zero, the graph intercepts the Y-axis right at the origin, as the black line does in panel (b).
Let's see if we can figure out the equation for the relationship depicted in Figure A.1. There, X denotes advertising and Y denotes sales. On the graph, it is easy to see that when advertising expenditure is zero, sales are $40,000. Therefore, our equation will have a vertical intercept of a = 40. Earlier, we calculated the slope of this graph to be 3. Therefore, the equation will have b = 3. Putting these two observations together, we find that the equation for the line in Figure A.1 is
Now if you need to know how much in sales to expect from a particular expenditure on advertising, you'd be able to come up with an answer: You'd simply multiply the amount spent on advertising by 3, add $40,000, and that would be your sales. To confirm this, plug in for X in this equation any amount of advertising from the left-hand column of Table A.1. You'll see that you get the corresponding amount of sales in the right-hand column.
Was this article helpful?