Difference Between Linear and Curvilinear Correlation

In statistical studies, we measure more than one variable for each individual. Like we measure precipitation and plant growth, or we measure the number of young birds with their nesting habitat. So, we collect pairs of data and study them together instead of studying the pair or variable individually. This gives rise to correlation.

Studying Correlation, We will Find Two Terms – Linear and Curvilinear Correlation. In this section, our motive is to explain the differences between these two terms, we will also define the terms under the heading ‘meaning of linear correlation’ and ‘what is curvilinear correlation?’ Hence, let us get started. 

Difference between Linear and Curvilinear Correlation

As already mentioned, we will prioritize our study on the difference between Linear and Curvilinear Correlation. Apart from this, it is important for us to know the meaning of correlation, linear correlation, and curvilinear correlation in depth. 

Well, in simple words we can say – Linear Correlation means the ratio of change that is constant. While Curvilinear Correlation or Non-Linear Correlation means the ratio of change is not constant. 

This is only a brief discussion of the difference between Linear and Curvilinear Correlation, we will represent the same in detail in our forthcoming section. 

The Bivariate Data

If we examine each variable separately, it means we are examining the univariate data, but in correlation, we find ways to describe and analyze the bivariate data, in which there are two variables. If you take a sample, we can describe the relationship between the two variables taken in the sample graphically and numerically. So, we can say correlation is defined as the statistical correlation between two variables.

Meaning of Linear Correlation

Linear correlation is referred to as the measure of relationship which is between two random variables with their values which range from -1 and 1. This is proportional to the covariance which can be interpreted in the same way as the covariance.

Linear correlation can also be said to be based on the straight-line relationship which occurs between two random variables given in the sample.

Correlation is known as linear if the ratio of change remains constant. Suppose, the amount of output in a factory gets doubled by doubling the number of workers, if the data is graphed it will be an example of linear correlation.

Graphically Represented - when all the points on the scatter diagram incline to lie near a line that looks like a straight line, then the correlation is said to be a linear equation. 

Non-linear, also known as the curvilinear correlation is said to occur when the ratio of change happens between two variables that are not constant. This can happen when the value of one variable increases, with the value of another variable also increasing side by side. This will happen to an extent, after which the increase in that value of one variable will start resulting in the decrease in the value of the other variable.

To represent the curvilinear equation graphically – It is an inverted U 

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Difference Between Linear and Curvilinear Correlation

The difference between linear and curvilinear correlation is depicted below with the help of a graph.

A Scatter Diagram Depicts many Relations between Two Variables 

A correlation happens to be between two variables only when one of them is related to the other in some or another way. We can take an example of a scatter diagram, which is a graph of the paired (x, y) sample data with the horizontal x-axis and with its vertical y-axis. Each individual (x, y) pair is plotted in the form of a single point.

Here, we plot the bear chest girth (y) against the bear length (x). When examining the scatter diagram, we need to study the overall pattern of the plotted points. We will find that the value for the chest girth tends to increase as the value of the length increases. Also, we will observe the upward slope and a straight-line pattern in the plotted data points illustrated in the graph.

Thus, we can say that a scatter diagram can identify several different types of relationships between any two related variables. 

The Relationships are as Follows:

• A relationship will have no correlation when the points on a scatter diagram do not show any specific pattern.

• A relationship is called non-linear when the points on the scatter diagram follow a pattern but the pattern is not a straight line.

• A relationship is called linear when the points on the scatter diagram give rise to a straight-line pattern.

• Linear relationships can be any - positive or negative. Positive relations have their points which are inclined upwards to the right side. If the value increases, the value of y increases. If the value of x decreases, the value of y decrease. 

• If there is a negative relationship then their points will decline downwards to the right. If the value of x increases, the value of y decreases. While, if the value of x decreases, the value of y increases. 

• Non-linear relationships will have a clear pattern, they are not only linear. 

• Also, to note – if two variables have no relationship, then there will be neither a straight-line relationship nor a non-linear relationship.