 Hi, my name is Rebecca. I'm studying Actuarial Studies and Economics at ANU. One of the main focus of Actuarial Studies is forecasting and modeling risk using available data. So I'm quite familiar with data analysis, and in this video we'll focus on interpreting data specifically the gradient of graphs. The gradient can be interpreted as the rate of change between a unit change of the dependent variable per unit change of the independent variable. We can find the gradient of the line of best fit by the following formula. Changing the dependent variable divided by changing the independent variable. Understanding the relationship between the dependent and independent variables is important when planning your experiments. During them and when drawing a graph, and it is also important when you're interpreting the data from any graph. The independent variable is the variable that we can alter in an experiment. It is not correlated with other variables, nor random errors. The independent variable, for example the temperature of the starting materials, the amount of time for something to grow, or the weight of a pendulum influences the dependent variable, what we're interested in measuring, for example the reaction time, growth of plant, or the force that a pendulum exerts. To look at this relationship more carefully, let's take an example. Suppose we did an experiment to find out the amount of caffeine content in chocolates. Say I did this test and gathered the following data. Perhaps you can see a general trend in the table of data. Caffeine level does go up with pieces of chocolate, but it's not smooth. We can see that better if we graph it. You can see that the independent variable pieces of chocolate is placed on the x-axis and the dependent variable caffeine content is placed on the y-axis. From just looking at the graph, we can see a clear positive correlation, which is expected as we know that every piece of chocolate contains a certain amount of caffeine. But how do we calculate the neuronal correlation between the two variables? Excel can help us to illustrate a line of best fit. Here we can see that Excel has helped us to produce the line of best fit. The blue dots illustrate the actual amount of caffeine that we have measured, which contains the random errors. The line of best fit is illustrated by the red line through the orange points, which are all predicted values that have adjusted for the random errors. We can find the gradient of the line of best fit by changing the dependent variable divided by changing the independent variable. So in our example, we can find the gradient by choosing two orange points. For example, the points 6 pieces of chocolate for 72.42 milligrams of caffeine, and 8 pieces of chocolate for 97.85 milligrams of caffeine. So the change in the dependent variable is 25.43 milligrams of caffeine, and the change in the independent variable is 2 pieces of chocolate. Therefore, the gradient is 12.715 milligrams of caffeine per piece of chocolate. This concept of gradient can be applied to other variables with linear relationship. Gradient is something that you can calculate quite easily from any line of best fit, whether it is in Excel or whether you have drawn your book. Do you think this linear relationship will continue forever? What will happen if we extended the experiment to 50 pieces of chocolate or 100? It is important to remember that statistics can be really useful, but to know the situation around the data and use our own analytical skills to decide when to rely on them and when not to.