Let's start with scatter plots. A scatter plot is a graph of past cost and activity data where each observation is represented by a dot ion the graph. Here is an example. Scatter plots are helpful in three primary ways. First, you can use them to get a sense of the behavior of a cost. For example, a scatter plot of a variable cost might look something like this. Trending generally upward, similar to what we saw earlier in the linear representation. And a scatter plot of a fixed cost might look something like this, Remaining essentially flat, similar to that earlier linear representation. Second, scatter plots can help you assess whether the relationship between a cost and activity can be captured by a straight line. There might not always be a clear trend line. Here's an example of a relationship that can be reasonably captured by a line. But, the other example is an example of a relationship that might not be well-represented or well-captured by a line. In the second case, where a line doesn't do a good job of capturing the relationship between a cost and activity, you would need to use more sophisticated techniques than we will discuss in this course. All right. Third, scatter plots can help you identify observations that might not be representative of the normal relationship between a cost and activity. Here is an example. In the first scatter plot, All these observations seem to fall within a similar pattern. However, in the other scatter plot, you can see these two observations that seem to be very different than the majority of observations. Observations like these are often called outliers. These are important to notice because as we try to estimate a line that captures the relationship between cost and activity, we don't want to allow those observations to have much influence on the resulting equation we come up with. Because outliers are special cases where something unusual happened so they're not representative of a normal relationship. So how does a scatter plot help us estimate a cost equation? Like this. I could use a straight-edge such as a ruler, to draw a line through the plot to approximate that linear relationship. And it would look something like this. I would look to see where it intersects the y-axis to get the fixed-cost number, or the B in the equation of the line. And in this example, it looks like the line intersects at approximately 40,000-ish dollars, so that's going to be my estimate of fixed cost. And then I would estimate the slope of the line to get the variable cost per unit, so I'm looking for the M In that equation. All right, so I'm going to go pick any points on the line. Let's do this here. This spot on the line, and I don't know, we'll do something like about right here on the line. And this point right here looks like it's got cost of about $60,000, For 5,000 units. And this point right here looks like a cost of about $80,000, At an activity level of about 10,000 units. If I want to calculate the slope of the line I'm going to take the change in the cost and I'm going to divide it by the change in the number of units. And in this example it looks like the costs go up by about $20,000 for every $5,000 increase, And for every 5,000 increase in the number of units. So up by $20,000 for a 5,000 increase in number of units. So my estimate of the variable cost per unit is at $20,000 divided by 5,000 units or, $4. So now, I can use all of this information to write the equation that helps us predict costs. Here, that equation would be y is equal to m, the slope of a line or the variable cost per unit, which is $4, Times the number of units or x, plus b, or the y intercept or estimate of fixed cost, which is $40,000. It's relatively easy, right? It wasn't a sophisticated technique, but it does give us an estimate that might be useful in predicting future costs.