The Science of Life

As promised last time , I am going to cover the basics of simple regression analysis.  It is simple because there is only one independent variable for the dependent variable. As a side note here, most of you are likely familiar with the phrase "correlation does not imply causation".  This statement, while true, is misleading.  Yes, it is true that not all correlations are causal, it is also true that all causation's are correlated.  Causation cannot occur without correlation, so correlation is the first necessary step to show causation, but it is also an insufficient step. For example, if we look at the graph of MLB wins on the y-axis and the ratio of runs scored to runs allowed on the x-axis, it is easily apparent that the ratio and the number of wins are highly correlated.  This is a causal relationship as well.  The more runs you score and the fewer runs you give up, the more you'll win, because the winner is the team who scores more runs than...

You'll remember last time , I covered hypothesis testing of proportions and the time before that , hypothesis testing of a sample with a mean and standard deviation.  This time, I'll cover the concept of confidence intervals. Confidence intervals are of the form μ 1-α ∈ (a, b) 1-α , where a and b are two numbers such that a<b, α is the significance level as covered in hypothesis testing, and μ is the actual population mean (not the sample mean). This is a the statement of there being a [(1-α)*100]% probability that the true population mean will be somewhere between a and b.  The obvious question is "How do we find a and b?".  Here, I will describe the process. Step 1. Find the Fundamental Statistics The first thing we need to find the fundamental statistics , the mean, standard deviation, and the sample size.  The sample mean is typically referred to as the point estimate by most statistics text books.  This is because the point estimate of the po...

This is an entry in the Basic Statistics Lecture Series which I have realized that I have failed to incorporate into the series so far, and I apologize for that.  This lecture is going to cover the basic calculations required for all of statistical analysis, on a fundamental level. When we collect statistical data, we typically collect it on a small part of the population as a whole.  The population is the entire group for which a sentiment holds true.  This small part of the population as a whole is called the sample of the population, or just sample for short.  The number of data points we collect -- the number of items in the sample -- is called the sample size, which is typically denoted by the letter n. In statistics, we typically calculate the arithmetic mean, which is the sum of all values divided by the sample size.  For the population as a whole, this is denoted by the greek letter μ (mu), and for a sample, it's denoted by x . The sample mean ...