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Student: Class: Date: Using Functions in Models and Decision Making: Regression in Linear and Nonlinear Functions V. A Student Activity Sheet 1: Analyzing Linear Regression Equations One factor that
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Hi it's Mr. Andersen and welcome to my podcast on the chi-squared test chi-squared test if you look at the equation lots of students get scared right away it's really simple once you figure it out so doesn't be scared away but chi-squared test especially in AP biology especially in science is very important, and it's a way to compare when you collect data is the variation in your data just due to chance or is it too due to one of the variables that you're actually testing and so the first thing you should figure out is what are the all these variables mean so the first one this right here stands for chi-squared and so this is developed way in the early part of the 1900s by Karl Pearson's chi-squared test so what is this then that is going to be a sum, so we're going to add up a number of values in a chi-squared test what is the last and for well that's going to be the data that you actually collect, and so we called that observed data and then the e values are going to be the expected values and so if you're ever doing an experiment you can actually figure out your expected values before you start, and then you just simply compare them to your observed values let me give you an example of that with these coins over here let's say I flip a coin a hundred times and I get sixty-two heads and I get thirty-eight tails well is that due to just chance or is there something wrong with the coin or the way that I'm flipping the coin and so the chi-squared test allows us to actually answer that and so what I'm thinking in my head is something called a null hypothesis and so if we're flipping a coin a hundred times and I think I said sixty-two heads and thirty-eight tails well that would be the observed value that we get in an experiment, but there'd also be expected values because you know that it should be 50 heads and 50 tails and so you use something called a null hypothesis in this case where are you saying that there's no statistical significant difference between the observed values and the expected frequencies that we expect to get and then what do we actually find and so its cool chi squared because we actually measure our data or look at our data, and we can see is there a statistical difference between those two the best way to get good at chi-squared is actually to do some problems before we get to that there are two terms that I have to define one is degrees of freedom and then one is critical values and so the whole point of a chi-squared test is either to accept or reject our null hypothesis and so you have to either exceed or don't exceed your critical value, but first we have to figure out where that number is in this big chart right here first thing is something called degrees of freedom so since we're comparing outcomes you have to have at least two outcomes in your experiment so in this case if we have heads and tails we have two outcomes that we could get, so we'll say that's two, and then you simply subtract the number one from that to...

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Using functions in models refers to the implementation of mathematical or computational functions to analyze and predict outcomes based on input data within a model framework.
Typically, researchers, analysts, and data scientists who develop predictive models or perform data analysis are required to file using functions in models, particularly in regulated industries or academic settings.
To fill out using functions in models, one must define the model inputs, choose the appropriate functions, implement them within the model environment, and ensure that the data is processed accurately to produce outputs.
The purpose of using functions in models is to create a structured method for analyzing data, enabling predictions, simulating scenarios, and gaining insights from complex datasets.
Information that must be reported when using functions in models includes the model assumptions, the functions used, input data sources, results obtained, and any limitations or uncertainties associated with the model outputs.
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