Justifying your prediction by writing a Confidence Argument

Justifying your prediction by writing a Confidence Argument

After you make a prediction, you are generally asked about your confidence in making that prediction. How do you state your prediction and provide supporting evidence to support your conclusion?

There are three mandatory parts to a confidence argument.

1) What is the R2 value? The R2 value tells us how well the model fits our data. R2 is a number between 0 and 1. The closer to 1, the stronger the model. Here are some basic guidelines for this class:

 If 0.7 < R2 < 1, that is considered a strong fit.  If 0.4 < R2 < 0.7, that is considered a moderate fit.  If 0 < R2 < 0.4, that is considered a weak fit. (You might even question whether or

not you can use the model to make predictions when your R2 value is so low.

Keep in mind that the R2 value does not tell us if our prediction is accurate. Our predictions will hardly ever be exact, and there is no way to predict the future with 100% accuracy. The R2 doesn’t tell us about our prediction at all! It tells us about the model we are using to make the prediction. So it is very possible for you to use a strong model to make a horrible prediction.

2) How far into the future/past are you predicting? You need to note exactly how many years into the future from your last data point you are looking (or how many years into the past from your first data point). Then you need to determine how the length of time impacts your confidence level.

A “rule of thumb” is that you should be concerned about predictions more than 25 years away from your data in either direction. 25 years is about enough time for generational/societal/technological shifts to occur that will likely impact your prediction. If you feel your prediction is too far away from the data, you must state WHY – what do you think might change in that time frame that would impact your prediction?

3) Real world support. This is often the most difficult part of the argument for students to write. You must provide some reasons for why you think the trend will continue (or reasons for why you think it will not).

Answers that are NOT acceptable for this portion of the argument are:

 “It makes sense.” I’m glad when things make sense to you, but you need to explain to your reader WHY/HOW they make sense. We can’t see into your mind!

 “The trend has been increasing/decreasing for the last ___ years, so I bet it will continue to do so.” This is faulty logic. The marriage rate in the US was going strong for many, many decades! Until the 60’s came, with free love, and all the sudden the trend changed.

**4) “Overall…” At the end of your argument you should always include a final sentence that sums up your overall confidence level. It’s helpful to start the sentence with “Overall…,” but you can write it however you wish.

Examples: Let’s look at some of the predictions made on the previous page for women’s world records in the mile run:

Prediction #1: What will the women’s world record be in 1999? We predicted it would be 246 seconds.

How much confidence do you have in your prediction?

(Part 1 of the confidence argument is in blue. Part 2 of the confidence argument is in red. Part three of the confidence argument is in green. In practice you will probably end up combining parts 2 and 3 on many occasions. The overall conclusion sentence is in orange.)

My R^2 value is .9342, which shows the model is a good fit for my data. I am only looking three years into the future from my data, which isn’t too long. I don’t think that women have reached the physical limits of how fast the female body can run a mile, so this is certainly possible. I do notice that the data points seem to be leveling off slightly toward the end of the graph. This may mean that my prediction is a little lower that what the actual record will be in 1999. Overall, I have moderately strong confidence in this prediction.

Prediction #2: When will the women’s world record be 3 minutes? We predicted that the women’s world record will be 3 minutes in the year 2070.

How much confidence do you have in your prediction?

(Part 1 of the confidence argument is in blue. Part 2 of the confidence argument is in red. Part three of the confidence argument is in green. In practice you will probably end up combining parts 2 and 3 on many occasions. The overall conclusion sentence is in orange.)

My R^2 value is .9342, which shows the model is a good fit for my data. I am predicting 74 years into the future from my data, which is a pretty long time. I don’t think it is physically possible for the female body to run a mile in three minutes. I think that before 2070 we will have reached the physical limits of the female body, making this prediction impossible. Therefore, I have no confidence in this prediction.

Note: As a teacher, I am not looking for every student to have the same answer. I am looking for every student to have a well constructed argument. To give you an example of how student answers can differ but still be correct, here is an alternative answer to the previous question:

My R^2 value is .9342, which shows the model is a good fit for my data. I am predicting 74 years into the future from my data, which is a pretty long time. Science is finding more and more ways to expand what the human body can do. I think we are just at the beginning of a performance enhancing drug revolution, that some day may allow our bodies to do things we never thought were possible. While I don’t think it’s very likely that a woman will be able to run a 3 minute mile in 2070, I think that it is possible. Therefore, I have some small confidence in this prediction.