The post Interrelationships of quantitative variables: Correlation and Regression appeared first on Plantlet.
]]>In the experiment, we measure the two continuous characters which are associated with each other. For example, the height of the plant and the temperature of the atmosphere. Accordingly, to understand the relationship between two such variables, we need to know how they are related and how the relationship can be expressed in a visual form.
The statistical technique to determine the relationship or association between two quantitative variables is called correlation. In other words, it determines the relationship between two quantitative variables. However, it does not prove that one particular variable causes the change in the other.
In correlation coefficient, we measure the degree of the relationship between two sets of figures in terms of another parameter. A simple correlation coefficient is denoted by the letter “r”. In addition, it is known as Pearson’s correlation or product-moment correlation coefficient. For population coefficient, we use the Greek letter “ρ”. Its pronunciation is “rho”. Certainly, the absolute value of r remains constant irrespective of change of origin.
The extent of correlation varies between minus one and plus one (-1 ≤ r ≤ 1). The value is in a fraction with a positive or negative sign.
Best safe and secure cloud storage with password protection
Get Envato Elements, Prime Video, Hotstar and Netflix For Free
Best Money Earning Website 100$ Day
#1 Top ranking article submission website
It is common to use a scatter diagram as a visual representation of data. We can show on a graph paper by plotting each pair of variables (X and Y). Consequently, placing a dot at the point corresponding to the values of X and Y.
The two variables are moderately proportional to one another.
This calculation is introduced by Professor Karl Pearson. It is used to determine the direction and degree of the linear relationship between two variables. The variables must be normally distributed for this method to be applied.
Formula:
Where numerator indicates variability between two variables.
As we carry out an experiment and take observations from the sample, the observed value of “r” has to be tested for significance. The following formula is for the calculation of a small sample. We set up null-hypothesis as:
H^{o }= There is no significant relationship between dependent and independent variables.
Formula:
where the degrees of freedom = n-2.
We use regression analysis to describe the relationships between a set of independent variables and the dependent variable. Regression analysis produces a regression equation. Moreover, the coefficients represent the relationship between each independent variable and the dependent variable. Therefore, it enables the user to predict the values of one variable on the basis of the other variable. For instance, on the positive or negative side, beyond the mean. Francis Galton coined the term “regression” in the nineteenth century. He described a biological phenomenon through regression.
The regression coefficient is denoted by the letter “b”. It shows the gradient or slope of the straight line of correlation. Moreover, it can calculate the equation for a straight line in correlation (Y= a+bX).
Formula:
The calculated b is placed into the equation. Consequently, “a” is a constant for Y-intercept. We can find by subtracting the product of regression coefficient and mean of X from the mean of Y:
Finally, we plot a straight line. Place the value of X and Y. The lines will go through the points.
Reference:
The post Interrelationships of quantitative variables: Correlation and Regression appeared first on Plantlet.
]]>