#linear correlation

The Quantitative Complexity Theory relies on a new, modern approach to correlation – the generalized correlation – which overcomes the well-known problems of mainstream approaches such as Pearson’s or Spearman’s correlation. The importance of correlation cannot be overstated. This is because the presence of a correlation imples the existence of a rule and rules are what make things work. By rules…

The dangers of linear correlation arise when oversimplifying relationships between variables, leading to flawed conclusions, misguided decisions, or hidden risks, see recent blog. Here’s a breakdown of key pitfalls: 1. Assuming Linearity in Nonlinear Relationships Risk: Linear correlation (e.g., Pearson’s r) quantifies only straight-line relationships. Many real-world relationships are…

“correlation is charlatanism”“Anything that relies on correlation is charlatanism” is a great article. But is correlation charlatanism? Yes it is. But it is not for the reasons explained in the article. Here is why. Correlations are present everywhere. The concept of correlation is one of the key constructs of statistics, modelling, simulation. It is used to design portfolios, to estimate risks,…

What is a Linear correlation?

Based on the nature of the relationship between the two variables, correlation can be broadly categorized into the following three types: Positive and Negative Correlation, Linear and Curvilinear Correlation, and Simple and Multiple Correlation. Linear correlation If the ratio for change between the two variables is constant or fixed, then the 2 variables are said to be linearly…

Here I am using the GapMinder dataset to examine the relationship between income per person and life expectancy using Pearson Correlation. In particular, I am interested to statistically establish the answer the below question:

Does life expectancy have a linear relationship with income per person?

Here, income per person is my independent predictor and life expectancy is considered the dependent variable. 

Pearson correlation coefficient (r) can have values ranging from -1 to +1 where

·        -1 denotes a perfect linear negative relationship

·        0 denotes no linear relationship at all

·        +1 denotes a perfect linear positive relationship

As a result, if r is +1 or -1 we can use the independent predictor variable to perfectly predict the values of the dependent variable. For any other values of r, we can calculate r2 (called coefficient of determination) to understand up to what percentage we can predict the variability of the dependent variable using the independent predictor.

Here is the code snippet in SAS:

Program Output

Observations and interpretations

1.     From the output of PROC CORR, the correlation coefficient has a value of approximately +0.6 which means the two variables have a fair correlation and life expectancy increases as income per person rises.

2.     The r2 value is 0.6 * 0.6 = 0.36 indicating that we can predict the variability in life expectancy by observing changes in income per person in only 36% cases.

do any of you know of a good place to get 20-50 real data points that are have a pretty strong linear correlation?