Hi friends! Today we will discuss about the Correlation & Regression with an example.
Correlation – discuss about how correlation measures the strength and direction of a relationship between two variables, emphasizing the concepts of positive, negative, and zero correlation.
Regression Analysis: Introduce regression analysis as a tool for predicting the value of one variable based on another, exploring linear regression and its components like slope and intercept.
Why are Correlation & Regression are used?
Medical Research and Healthcare: In medical research, correlation and regression are employed to analyse relationships between variables, such as the correlation between smoking and lung cancer. Regression models can be used to predict health outcomes based on various factors.
Quality Control in Manufacturing: These analyses are used in manufacturing to identify factors affecting product quality. For instance, regression analysis can help determine which variables contribute to defects in a manufacturing process.
Scientific Research: In various scientific disciplines, correlation and regression analysis play a crucial role in examining cause-and-effect relationships and making predictions based on observed data.
For performing correlation and regression, two sets of data, X and Y, are required. Both X and Y data should be variable.
Let’s understand this with an example.
Open Minitab:
Path Stat>Basic Statistics> Correlation> then select variables. First, select the X variable (Temp), then the Y variable (Seal), and finally, click on OK.
Now we can see the r= 0.913, r is called Co-relation coefficient (r). The correlation coefficient of 0.913 between “Seal (g/cm2)” and “Temp (F)” suggests a very strong positive correlation. This indicates that as the temperature increases, the seal density (g/cm2) tends to increase as well, and vice versa. The high correlation coefficient of 0.913 signifies a robust relationship, and the association is statistically significant. We can say X (Temp) is a root cause.
Co-relation coefficient (r)
r = 1 (Strong relationship between X & Y)
r = 0 (No relationship between X&Y)
r = -1 (Weak relationship between X & Y)
Co -relation coefficient ranges from -1 to 1.
In the above example, if we wish to set the temperature and observe the corresponding seal strength, an equation is necessary.
Path –
Stat >Regression > fitted line plot Then, select “Response Y” as Seal and “Predictor X” as Temp, as shown in the picture below. Choose the type of regression model as Linear.
Here we get the equation as mentioned below.
The regression equation is
Seal (g/cm2) = 101.6 + 0.3542 Temp (F)
We can also write.
Y = a +bX
It is also called Simple linear regression.
Now put the value of( X) temp as 250°C and get the value of Y.
Seal (g/cm2) = 101.6 +0.3542* 250 = 190.15