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Correlation gives us a numeric value to the degree and direction to which any two variables are related. It simply tells us how much one variable tends to change when the other one does. With correlation, one doesn't have to think about cause and effect. The matter isn’t about which out of the two variables is dependent or which is independent. What matters is that even if the two variables swapped the degree of correlation, the coefficient will be the same. Simple linear regression finds the line which best predicts the dependent variable from the independent variable. To know which variable is dependent and which is independent is quite important for linear regression. The line predicting the independent variable from the dependent variable is not the same as the line predicting the dependent variable from the independent variable. In this article, we will learn about differences in correlation and regression, what are correlation and regression and different types of correlation and regression.
| Table of Content |
Key Takeaways: Correlation, Regression, Line of regression, Positive Correlation, Negative Correlation, Dependent and Independent Variables
What is Correlation?
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Correlation is a combination of two words, that is 'Co' meaning together and the relation between two quantities. We observe correlation when there is a change in a unit in one variable and this is retaliated by an equivalent change in the other variable, that can be, direct or indirect, at the time of study of two variables.
The variables can be uncorrelated if the motion of one variable does not amount to any movement in a specific direction for another variable. This represents the strength of the linkage between variable pairs.
The correlation is either positive or negative. For example, if two variables move in the same direction, i.e., the increase in one variable brings a corresponding increase in another variable, and vice versa, then the variables are correlated positively like Investment and profit.
A Negative correlation is when the two variables move in different directions and for an increase in one variable, there is a decline in another variable and vice versa. For example, Product price and demand.
Correlation can be measured as:
- Karl Pearson’s Product-moment correlation coefficient
- Spearman’s rank correlation coefficient
- Scatter diagram
- Coefficient of concurrent deviations
What is Regression?
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Regression can be known as a statistical technique used for estimating the change in the metric dependent variable, this is based on the average mathematical relationship between two or more variables. It is important for many human activities as it is a powerful and flexible tool that helps forecast past, present, or future events depending on past or present events. To give an example, we can calculate how much profit a business can do in the future based on its past records. X and Y, the two variables are in a simple linear regression, where y is dependent on x or is influenced by x. Here y is the variable dependent or criterion, and x is an independent variable or predictor. The line of regression y on x is depicted as:
y = a + bx
Here, a = constant and b = regression coefficient.
In this equation, a and b are the two regression parameters.
Types of Correlation
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On the basis of their nature, the types of correlation are:
- Positive Correlation: This is when two variables move in the same direction, and when the value of one increases, it results in an increase in the other, and vice versa.
- Negative Correlation:When two variables are seen moving in different directions, and in a manner that any increase in one variable results in a decrease in value of the other, and vice versa, then the variables are said to be in negative correlation.
- Zero Correlation: If any given change in a variable is not dependent on the other it is said to be Zero Correlation, e.g., marks and height of students in a class.
Correlation can be either positive or negative.
Types of Correlation
Types of Regression
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The different types of regression based on their functionality are as follows:
- Simple linear Regression: This regression is used to study the relationship between any two continuous variables – an independent variable and a dependent variable.
- Multiple Linear Regression: In this regression, the relationship which is examined is linear and exists between a dependent variable and more than one independent variable.
Correlation Vs Regression
Differences Between Correlation and Regression
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The differences between correlation and regression are:
| BASIS | CORRELATION | REGRESSION |
|---|---|---|
| Definition | Correlation gives the co-relationship or association or interconnection between the two variables. It is a statistical measure. | ‘Regression’ describes how the independent variable is associated numerically with the dependent variable. |
| Usage | Represents a linear relationship between two variables. | Used to fit the best line and estimate the value of one variable based on its relationship with the other. |
| Dependent/Independent Variables | There is no difference between dependent and independent variables. | Both variables are different from each other. |
| Indicator | It depicts the way of movement or extent to which the two variables move together. | Regression is an indicator of the impact of a unit change in the variable which is known (x) on the estimated variable (y). |
| Objective | It defines the numerical value which depicts the relation between variables | It estimates the value of the random variable based on the values of the fixed variable. |
| Purpose | Its primary purpose is to give the value of the most dependable forecasts. | The purpose is to predict unknown variables based on the known variable. |
| Scope | It has limited applications. | It has a broader scope of applications. |
| Range | Coefficients may range from -1.00 to +1.00. | If byx > 1, then bxy < 1 in regression analysis. |
| Responding nature | The coefficient of correlation is independent of any change of Scale or shift in Origin. | The coefficient of regression is dependent on the change of Scale but is independent of its shift in Origin. |
| Nature of coefficient | The correlational coefficient is mutual and symmetric. | This coefficient fails to be symmetrical. |
| Exceptional treatment | In some correlational analyses, non-sense correlation finds its place. | In regression analysis non-sense regression is non-existent. |
| Mathematical treatment | It’s not quite useful for advanced mathematical treatment. | Used widely for advanced mathematical treatment. |
| Relationships | Correlation relationships are confined to the linear relationships existing between only the variables. | This encompasses linear and non-linear relationships both. The cause-and-effect relationship between the two variables is indicated, and a functional link is established. |
| Variables | Both variables x and y are random variables. | The variable x is a random variable while y is a fixed variable in the regression. There might be times when both the variables may be random variables. |
| Co-efficient | It serves to be a relative measure. | The coefficient of regression is generally an absolute figure. |
Things to Remember
- Correlation quantifies the direction and strength of the relationship between two numeric variables, X and Y, and always lies between -1.0 and1.0.
- Simple linear regression relates X to Y through an equation of the form Y = a bX.
- There's a relationship between the variables when it comes to correlation. In discrepancy, regression places emphasis on how one variable affects the other.
- Correlation doesn't capture reason whilst it's grounded on regression.
- The correlation between x and y is identical to that between y and x. Contrary to this, a regression of x and y, and y and x are quite different.
- Eventually, one single point is a graphical representation of a correlation. Whereas one line visualizes a direct regression.
Sample Questions
Ques 1. What are the advantages of correlational and regression analysis? (2 Marks)
Ans. Advantage of Correlation Analysis:
This type of analysis gives one a clear and more concise summary of the relation between two variables.
Advantage of Regression Analysis:
Regression analysis is very advantageous as it lets one take a clear, detailed and calculated look at the data and it also includes an equation that is used to predict and optimize the data set in the future.
Ques 2. When should I use regression analysis? (3 Marks)
Ans. When you wish to estimate a nonstop dependent value from a set of independent factors, you use regression analysis. Logistic regression should be used if the dependent variable is dichotomous. (Both logistic and direct regression will produce analogous findings if the split then between two situations of the dependent variable is close to 50-50.) In regression, the independent variables could be either nonstop or dichotomous. In regression analysis, independent variables with far further than two situations can be employed, but they must first be converted into variables with just two situations.
Ques 3. Describe the conditions in which correlation and regressions are to be used. (3 Marks)
Ans. Correlation and regression are two different mathematical quantities that can be used under various conditions like:
- Correlation: We use this measure when we have an immediate requirement to understand a direction. There will be a relation between two or more variables involved.
- Regression: It is used as a measure used when we have a requirement to optimize and explain the numerical response provided from y to x. This helps us understand how y influences x by creating an approximation.
Ques 4. Write a short note on Correlation and Regression. (3 Marks)
Ans. The differences between correlation and regression, which are two extremely two crucial mathematical concepts, are not studied independently of each other. When a researcher needs to assess if the variables he is studying are directly or indirectly correlated or not, they use correlation analysis. If they are correlated, then this analysis shows the strength of their association. One of the most popular measures of correlation is known as Pearson’s correlation coefficient.
For, regression analysis, establishing a functional relationship between a pair of given variables with the intent of making future projections concerning events is required.
Ques 5. What is the difference between correlation and regression slope? (3 Marks)
Ans. Correlation measures the direction and strength of the association between two numeric variables, X and Y, which always comes out to be between -1.0 and 1.0.
Y = a + bX, a simple linear regression equation connects X with Y.
Both these analyses measure the degree and direction of a link between two numeric variables X and Y. The regression slope (b) is negative when the correlation (r) is negative. The regression slope is positive if the correlation is positive.
Ques 6. List some key similarities between correlation and regression. (5 Marks)
Ans. Some similarities between correlation and regression are:
- They both are responsible for quantifying the direction and strength of the relationship between any two numeric variables.
- The correlation (r) when negative, the regression slope (b) will be negative.
- The correlation when positive, the regression slope will be positive.
- When the correlation is squared (r2 or R2) it has special meaning in simple linear regression as it represents the proportion of variation in Y which is explained by X.
Ques 7. Why is it important for us to learn the difference between Correlation and Regression? (2 Marks)
Ans. Correlation and regression are some of the most important topics for the students of class 12. We find its application in statistics and it allows finding various relations and values for different variables involved. Both correlation and regression are necessary and play important roles in different situations, therefore it is necessary to analyse and understand under which conditions are to be used and which measures. We will be able to calculate the answer effectively and apply the logic learned.
Ques 8. Write a note on different types of Correlation according to their character. (3 Marks)
Ans. The three types of relation to their character are -
Positive Correlation – when two variables are seen moving in the same direction, and there is an increase in the value of one variable that results in an increase in another, and vice versa.
Negative Correlation – if the two variables are moving in different directions, when there is an increase in any way in one variable it results in a decrease in the value of the other, and vice versa.
Zero Correlation - If any change in one variable is not dependent on the other, then it is Zero Correlation.
Ques 9. What is the mean for X and Y variables and the coefficient of correlation between them in the following two regression equations? (5 Marks)
(1)2y–x–50 = 0
(2)3y–2x–10 = 0.
Ans. Given,
2y–x–50 = 0 ... (1)
3y–2x–10 = 0 ... (2)
Solving equations (1) and (2)
We get, Y = 90
Then, putting the value of Y in equation (1)
We get, X = 130
Next is to calculate correlation coefficient
Assume equation (1) be the regression equation of y on x
2Y = X+50
Remember,
In the above-given problem one of the regression coefficients is greater than 1 while the other is less than 1. Therefore, what we assumed for the given equations are correct.
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