Making the grade

1. Making the grade

We rely on predictions every day. Weather, traffic, email, and other daily benefits and nuisances use past information to predict future conditions. There's just one problem: we can best predict the future when it closely resembles the past, which is not always the case.

2. Predicting students' grades

In this chapter, we'll use a dataset that contains students' grades from the first and second term, their mother's level of education, the number of classes they missed, and their final grade. You will use this information in the exercises to make predictions about students' final grades. Which of these factors do you expect are closely tied to students' final grades?

3. Weighted averages vs. linear models

We'll explore a couple of methods for predicting students' grades: weighted averages and linear models. Let's start with weighted averages. Weighted averages are appropriate when we have interim measures that lead to a final summary statistic, as is the case with our term 1 and 2 grades along with our final grades. We can adjust the weights in our weighted average to put more emphasis on one interim measure. For example, we can create a weighted average that computes an expected final grade and assign more weight to period 1 or period 2 grades. As we shift these weights (i.e., increase the relative importance of one factor), we'll see our weighted average change.

4. Weighted averages vs. linear models

Alternatively, you can think of linear models as the lines of best fit, which you may have calculated before. They try to find an algebraic equation that calculate a line that best represents a linear (or algebraic) relationship between the thing you're predicting and the data you're using to predict it. One key difference is that weighted averages only take into account students' own scores whereas linear models use data from individual students, as well as their peers, to make predictions.

5. Prediction methods

Let's quickly cover some pros and cons of these two types of these predictions. Weighted averages are straightforward and accurate when we have linked measures (like students' term grades and final grades), but they are inappropriate for generalizing from unrelated data. For example, weighted averages can't help us predict student's final grades based on the number of absences students had. On the other hand, linear models can generalize relationships between various pieces of data and make reasonable predictions in novel situations. However, they may oversimplify these relationships. For example, a linear model can help us predict final grades based on parental education levels, but the model tries to represent something complex (i.e., the impact of parents' education on students' grades) with an overly simple straight line.

6. Weighted averages

Since we have interim measures (that is, period 1 and 2 grades, as well as final grades), we'll concentrate on weighted averages for now. They require a number of values and the same number of weights. The values are the cells that contain the data you want to average. The weights are the proportions that you want to apply to these different values (e.g., 80% to period 1 grades or 60% to period 2 grades) The sum of the weights should equal 100, but Spreadsheets will scale them proportionally if not.

7. Weighted averages

We can add a simple formula to make the second weight 100 minus the first weight. Now we can reference these two cells see the impact of adjusting these weights without rewriting our formulas each time.

8. Weighted averages

Here, we're just looking at the weighted average of grades from the first and second term.

9. Weighted averages

The weights are set at 50% each, which is actually an unweighted average. That is, each period 1 grade is worth as much as each period 2 grade, so each predicted final grade is just the average grade between period 1 and 2 for each student.

10. Let's practice!

You'll get to calculate and adjust these weights in the exercises that follow. We've thrown a lot at you; we predict it will help you complete the exercises up next!

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