Statistics and Regression Analysis in Calculus
Statistically-evidential (SD) models are designed to forecast future values based on past data. This form of statistical inference is widely used by forecasting agencies and actuaries. For example, if you want to know how much you can earn over the next two weeks, then you’d use a statistical model to estimate how income will be a week from now, based on the information you have today. You would then apply this information to the regression trends you observe in your data set to get an estimate of what you’d earn in future weeks. SD models take a sample of the past to create a statistical estimate of what the future might be like based on the past.
Regression analysis on the other hand uses a statistical model to predict the parameters of a particular variable over time. This form of statistical inference is often used in environmental studies, where researchers attempt to predict change in a variable over time. One example of a regression study might look at the relationship between temperature and humidity over time or rainfall and drought. Over time, there’s a strong relationship between these variables and the severity of droughts and extreme temperatures. By averaging the data over time, we can predict where future temperatures may be and what effect they may have.
Once you’ve applied these two forms of statistical inference to your data set, you’re ready to test your hypothesis. The problem with regression analysis, however, is that it typically involves many steps. It takes quite some time to run all the steps necessary to make a reasonable estimate of the distribution of parameters. In cases where the number of steps to estimate the distribution of parameters is relatively small, this can significantly reduce the speed at which you’ll examine your data and arrive at a reasonable estimate of the distribution of parameters. As a result, this form of statistical inference often involves using Monte Carlo techniques or other random number generators in order to draw a reliable outcome from the information you’re studying.
In an economic theory course, you’ll learn many examples of regression analyses. In particular, you’ll study the famous chicken example mentioned above. What do you know about chickens in particular? You probably know that they are sociable animals who enjoy living in groups of up to ten or twelve members. For this reason, if you suspect that a change in the number of egg laying hens is correlated with the change in the profitability of the chicken industry, you should be able to use the information on the distribution of characteristics of chicken hens to make a statistical analysis and determine if that hypothesis is correct.
Fortunately, because economic theory courses typically begin to explore the topics of regression analysis, you won’t have to worry about learning anything about chicken production until you’re done with the course. Once you’ve learned about the chicken example used above, you can use the information on the distribution of characteristics of chicken to make a regression analysis to see if your hypothesis was true. Once you understand how to perform a regression analysis, you can examine nearly any kind of real-world data, including sales records, census records, property records, stock ownership and sales price data. A regression analysis, when performed correctly, will provide a reliable estimate of the relationship between any variable and any other variable. Because regression is an economic theory concept, however, there are many different ways in which a regression analysis can be performed.
Of course, you can also use other types of statistical inference and regression analysis in your exam preparations, although most teachers expect you to learn the methods used in economic theory classes. In these situations, you’ll probably need some additional practice in order to become comfortable with the concepts of statistical inference and regression analysis. You can find plenty of practice questions on the exams of the AP Calculus AB exam online, and you can study for your exams using practice tests and guides. However, don’t forget that the topics you cover in your Calculus classes, such as limits, derivatives, quadratic equations and more, are covered in much greater depth when you take the Calculus AB exam.
When I took the Calculus AB exam, I also re-took my physics class and focused on topics that would help me understand the concepts used in statistical inference and regression analysis more thoroughly. After learning about logistic regression and running a data set, I had a better idea of what I needed in order to pass the test. And while I didn’t pass the first time, I learned from every class I took and passed with flying colors. The two Calculus classes I took made me a better student, but they didn’t prepare me for the Calculus AB exam. By studying for and taking the actual exam, I was able to score nearly a 500 percent higher than the average student. This makes me highly qualified to take my exam for me.