1669003919

In this article, let's learn about Differences between Covariance vs Correlation. In statistics, covariance and correlation are two mathematical notions. Both phrases are used to describe the relationship between two variables. This blog talks about covariance vs correlation: what’s the difference? Let’s get started!

Covariance and correlation are two mathematical concepts used in statistics. Both terms are used to describe how two variables relate to each other. Covariance is a measure of how two variables change together. The terms covariance vs correlation is very similar to each other in probability theory and statistics. Both the terms describe the extent to which a random variable or a set of random variables can deviate from the expected value. But what is the difference between covariance vs correlation? Let’s understand this by going through each of these terms.

It is calculated as the covariance of the two variables divided by the product of their standard deviations. Covariance can be positive, negative, or zero. A positive covariance means that the two variables tend to increase or decrease together. A negative covariance means that the two variables tend to move in opposite directions.

A zero covariance means that the two variables are not related. Correlation can only be between -1 and 1. A correlation of -1 means that the two variables are perfectly negatively correlated, which means that as one variable increases, the other decreases. A correlation of 1 means that the two variables are perfectly positively correlated, which means that as one variable increases, the other also increases. A correlation of 0 means that the two variables are not related.**Contributed by: ****Deepak Gupta**

*If you are interested in learning more about Statistics, taking up a free online course will help you understand the basic concepts required to start building your career. At Great Learning Academy, we offer a **Free Course on Statistics for Data Science**. This in-depth course starts from a complete beginner’s perspective and introduces you to the various facets of statistics required to solve a variety of data science problems. Taking up this course can help you power ahead your data science career.*

In statistics, it is frequent that we come across these two terms known as covariance and correlation. The two terms are often used interchangeably. These two ideas are similar, but not the same. Both are used to determine the linear relationship and measure the dependency between two random variables. But are they the same? **Not really. **

Despite the similarities between these mathematical terms, they are different from each other.

Covariance is when two variables vary with each other, whereas Correlation is when the change in one variable results in the change in another variable.

In this article, we will try to define the terms correlation and covariance matrices, talk about covariance vs correlation, and understand the application of both terms.

Covariance signifies the direction of the linear relationship between the two variables. By direction we mean if the *variables* are directly proportional or inversely proportional to each other. (Increasing the value of one variable might have a positive or a negative impact on the value of the other variable).

The values of covariance can be any number between the two opposite infinities. Also, it’s important to mention that covariance only measures how two variables change together, not the dependency of one variable on another one.

The value of covariance between 2 variables is achieved by taking the summation of the product of the differences from the means of the variables as follows:

The upper and lower limits for the covariance depend on the variances of the variables involved. These variances, in turn, can vary with the scaling of the variables. Even a change in the units of measurement can change the covariance. Thus, covariance is only useful to find the direction of the relationship between two variables and not the magnitude. Below are the plots which help us understand how the covariance between two variables would look in different directions.

**Example:**

X | Y |

10 | 40 |

12 | 48 |

14 | 56 |

8 | 32 |

**Step 1: Calculate Mean of X and Y **

Mean of X ( μx ) : 10+12+14+8 / 4 = 11

Mean of Y(μy) = 40+48+56+32 = 44

**Step 2: Substitute the values in the formula **

xi –x̅ | yi – ȳ |

10 – 11 = -1 | 40 – 44 = – 4 |

12 – 11 = 1 | 48 – 44 = 4 |

14 – 11 = 3 | 56 – 44 = 12 |

8 – 11 = -3 | 32 – 44 = 12 |

**Substitute the above values in the formula **

Cov(x,y) = (-1) (-4) +(1)(4)+(3)(12)+(-3)(12)

___________________________

4

**Cov(x,y) =** 8/2 =** 4 **

**Hence, Co-variance for the above data is 4 **

**Quick check – **Introduction to Data Science

Correlation analysis is a method of statistical evaluation used to study the strength of a relationship between two, numerically measured, continuous variables.

It not only shows the kind of relation (in terms of direction) but also how strong the relationship is. Thus, we can say the correlation values have standardized notions, whereas the covariance values are not standardized and cannot be used to compare how strong or weak the relationship is because the magnitude has no direct significance. It can assume values from -1 to +1.

To determine whether the covariance of the two variables is large or small, we need to assess it relative to the standard deviations of the two variables.

To do so we have to normalize the covariance by dividing it with the product of the standard deviations of the two variables, thus providing a correlation between the two variables.

The main result of a correlation is called the correlation coefficient.

The correlation coefficient is a dimensionless metric and its value ranges from -1 to +1.

The closer it is to +1 or -1, the more closely the two variables are related.

If there is no relationship at all between two variables, then the correlation coefficient will certainly be 0. However, if it is 0 then we can only say that there is no linear relationship. There could exist other functional relationships between the variables.

When the correlation coefficient is positive, an increase in one variable also increases the other. When the correlation coefficient is negative, the changes in the two variables are in opposite directions.

**Example: **

X | Y |

10 | 40 |

12 | 48 |

14 | 56 |

8 | 32 |

**Step 1: Calculate Mean of X and Y **

Mean of X ( μx ) : 10+12+14+8 / 4 = 11

Mean of Y(μy) = 40+48+56+32/4 = 44

**Step 2: Substitute the values in the formula **

xi –x̅ | yi – ȳ |

10 – 11 = -1 | 40 – 44 = – 4 |

12 – 11 = 1 | 48 – 44 = 4 |

14 – 11 = 3 | 56 – 44 = 12 |

8 – 11 = -3 | 32 – 44 = 12 |

**Substitute the above values in the formula **

Cov(x,y) = (-1) (-4) +(1)(4)+(3)(12)+(-3)(12)

___________________________

4

**Cov(x,y) =** 8/2 =** 4 **

**Hence, Co-variance for the above data is 4 **

**Step 3: Now substitute the obtained answer in Correlation formula **

Before substitution we have to find standard deviation of x and y

Lets take the data for X as mentioned in the table that is 10,12,14,8

To find standard deviation

**Step 1: Find the mean of x that is x̄**

10+14+12+8 /4 = 11

**Step 2: Find each number deviation: Subtract each score with mean to get mean deviation**

10 – 11 = -1 |

12 – 11 = 1 |

14 – 11 = 3 |

8 – 11 = -3 |

**Step 3: Square the mean deviation obtained **

-1 | 1 |

1 | 1 |

3 | 9 |

-3 | 9 |

**Step 4: Sum the squares **

1+1+9+9 = 20

**Step5: Find the variance **

**Divide the sum of squares with n-1 that is 4-1 = 3 **

20 /3 = 6.6

**Step 6: Find the square root**

Sqrt of 6.6 = 2.581

**Therefore, Standard Deviation of x = 2.581**

**Find for Y using same method **

The Standard Deviation of y = 10.29

Correlation = 4 /(**2.581** x10.29 )

Correlation = 0.15065

So, now you can understand the difference between Covariance vs Correlation.

- Covariance is used in Biology – Genetics and Molecular Biology to measure certain DNAs.
- Covariance is used in the prediction of amount investment on different assets in financial markets
- Covariance is widely used to collate data obtained from astronomical /oceanographic studies to arrive at final conclusions
- In Statistics to analyze a set of data with logical implications of principal component we can use covariance matrix
- It is also used to study signals obtained in various forms.

- Time vs Money spent by a customer on online e-commerce websites
- Comparison between the previous records of weather forecast to this current year.
- Widely used in pattern recognition
- Raise in temperature during summer v/s water consumption amongst family members is analyzed
- The relationship between population and poverty is gauged

- The graphic method
- The scatter method
- Co-relation Table
- Karl Pearson Coefficient of Correlation
- Coefficient of Concurrent deviation
- Spearman’s rank correlation coefficient

Before going into the details, let us first try to understand variance and standard deviation.

**Quick check –** Statistical Analysis Course

Variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of numbers are spread out from their average value.

Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. It essentially measures the absolute variability of a random variable.

Covariance and correlation are related to each other, in the sense that covariance determines the type of interaction between two variables, while correlation determines the direction as well as the strength of the relationship between two variables.

Both the Covariance and Correlation metrics evaluate two variables throughout the entire domain and not on a single value. The differences between them are summarized in a tabular form for quick reference. Let us look at Covariance vs Correlation.

Covariance | Correlation |

Covariance is a measure to indicate the extent to which two random variables change in tandem. | Correlation is a measure used to represent how strongly two random variables are related to each other. |

Covariance is nothing but a measure of correlation. | Correlation refers to the scaled form of covariance. |

Covariance indicates the direction of the linear relationship between variables. | Correlation on the other hand measures both the strength and direction of the linear relationship between two variables. |

Covariance can vary between -∞ and +∞ | Correlation ranges between -1 and +1 |

Covariance is affected by the change in scale. If all the values of one variable are multiplied by a constant and all the values of another variable are multiplied, by a similar or different constant, then the covariance is changed. | Correlation is not influenced by the change in scale. |

Covariance assumes the units from the product of the units of the two variables. | Correlation is dimensionless, i.e. It’s a unit-free measure of the relationship between variables. |

Covariance of two dependent variables measures how much in real quantity (i.e. cm, kg, liters) on average they co-vary. | Correlation of two dependent variables measures the proportion of how much on average these variables vary w.r.t one another. |

Covariance is zero in case of independent variables (if one variable moves and the other doesn’t) because then the variables do not necessarily move together. | Independent movements do not contribute to the total correlation. Therefore, completely independent variables have a zero correlation. |

Both Correlation and Covariance are very closely related to each other and yet they differ a lot.

When it comes to choosing between Covariance vs Correlation, the latter stands to be the first choice as it remains unaffected by the change in dimensions, location, and scale, and can also be used to make a comparison between two pairs of variables. Since it is limited to a range of -1 to +1, it is useful to draw comparisons between variables across domains. However, an important limitation is that both these concepts measure the only linear relationship.

*If you wish to learn more about statistical concepts such as covariance vs correlation, upskill with Great Learning’s **PG program in Data Science and Business Analytics.** The PGP DSBA Course is specially designed for working professionals* *and helps you power ahead in your career. You can learn with the help of mentor sessions and hands-on projects under the guidance of industry experts*. *You will also have access to career assistance and 350+ companies*. *You can also check out Great Learning Academy’s **free online certificate courses**.*

Original article source at: https://www.mygreatlearning.com

#**Covariance #Correlation **

1583920564

Let’s dive right in as I review correlation vs causation psychology and describe the main differences between these two common terms Are there any other correlation and causation examples you’d like to hear more about on the Troop Messenger blog Is there correlation vs causation analyses that you’re interested in within the broader realm of digital marketing and search engine optimization Let us know in the comments

#correlation vs causation, causation vs correlation, correlation vs causation examples #correlation

1669003919

In this article, let's learn about Differences between Covariance vs Correlation. In statistics, covariance and correlation are two mathematical notions. Both phrases are used to describe the relationship between two variables. This blog talks about covariance vs correlation: what’s the difference? Let’s get started!

Covariance and correlation are two mathematical concepts used in statistics. Both terms are used to describe how two variables relate to each other. Covariance is a measure of how two variables change together. The terms covariance vs correlation is very similar to each other in probability theory and statistics. Both the terms describe the extent to which a random variable or a set of random variables can deviate from the expected value. But what is the difference between covariance vs correlation? Let’s understand this by going through each of these terms.

It is calculated as the covariance of the two variables divided by the product of their standard deviations. Covariance can be positive, negative, or zero. A positive covariance means that the two variables tend to increase or decrease together. A negative covariance means that the two variables tend to move in opposite directions.

A zero covariance means that the two variables are not related. Correlation can only be between -1 and 1. A correlation of -1 means that the two variables are perfectly negatively correlated, which means that as one variable increases, the other decreases. A correlation of 1 means that the two variables are perfectly positively correlated, which means that as one variable increases, the other also increases. A correlation of 0 means that the two variables are not related.**Contributed by: ****Deepak Gupta**

*If you are interested in learning more about Statistics, taking up a free online course will help you understand the basic concepts required to start building your career. At Great Learning Academy, we offer a **Free Course on Statistics for Data Science**. This in-depth course starts from a complete beginner’s perspective and introduces you to the various facets of statistics required to solve a variety of data science problems. Taking up this course can help you power ahead your data science career.*

In statistics, it is frequent that we come across these two terms known as covariance and correlation. The two terms are often used interchangeably. These two ideas are similar, but not the same. Both are used to determine the linear relationship and measure the dependency between two random variables. But are they the same? **Not really. **

Despite the similarities between these mathematical terms, they are different from each other.

Covariance is when two variables vary with each other, whereas Correlation is when the change in one variable results in the change in another variable.

In this article, we will try to define the terms correlation and covariance matrices, talk about covariance vs correlation, and understand the application of both terms.

Covariance signifies the direction of the linear relationship between the two variables. By direction we mean if the *variables* are directly proportional or inversely proportional to each other. (Increasing the value of one variable might have a positive or a negative impact on the value of the other variable).

The values of covariance can be any number between the two opposite infinities. Also, it’s important to mention that covariance only measures how two variables change together, not the dependency of one variable on another one.

The value of covariance between 2 variables is achieved by taking the summation of the product of the differences from the means of the variables as follows:

The upper and lower limits for the covariance depend on the variances of the variables involved. These variances, in turn, can vary with the scaling of the variables. Even a change in the units of measurement can change the covariance. Thus, covariance is only useful to find the direction of the relationship between two variables and not the magnitude. Below are the plots which help us understand how the covariance between two variables would look in different directions.

**Example:**

X | Y |

10 | 40 |

12 | 48 |

14 | 56 |

8 | 32 |

**Step 1: Calculate Mean of X and Y **

Mean of X ( μx ) : 10+12+14+8 / 4 = 11

Mean of Y(μy) = 40+48+56+32 = 44

**Step 2: Substitute the values in the formula **

xi –x̅ | yi – ȳ |

10 – 11 = -1 | 40 – 44 = – 4 |

12 – 11 = 1 | 48 – 44 = 4 |

14 – 11 = 3 | 56 – 44 = 12 |

8 – 11 = -3 | 32 – 44 = 12 |

**Substitute the above values in the formula **

Cov(x,y) = (-1) (-4) +(1)(4)+(3)(12)+(-3)(12)

___________________________

4

**Cov(x,y) =** 8/2 =** 4 **

**Hence, Co-variance for the above data is 4 **

**Quick check – **Introduction to Data Science

Correlation analysis is a method of statistical evaluation used to study the strength of a relationship between two, numerically measured, continuous variables.

It not only shows the kind of relation (in terms of direction) but also how strong the relationship is. Thus, we can say the correlation values have standardized notions, whereas the covariance values are not standardized and cannot be used to compare how strong or weak the relationship is because the magnitude has no direct significance. It can assume values from -1 to +1.

To determine whether the covariance of the two variables is large or small, we need to assess it relative to the standard deviations of the two variables.

To do so we have to normalize the covariance by dividing it with the product of the standard deviations of the two variables, thus providing a correlation between the two variables.

The main result of a correlation is called the correlation coefficient.

The correlation coefficient is a dimensionless metric and its value ranges from -1 to +1.

The closer it is to +1 or -1, the more closely the two variables are related.

If there is no relationship at all between two variables, then the correlation coefficient will certainly be 0. However, if it is 0 then we can only say that there is no linear relationship. There could exist other functional relationships between the variables.

When the correlation coefficient is positive, an increase in one variable also increases the other. When the correlation coefficient is negative, the changes in the two variables are in opposite directions.

**Example: **

X | Y |

10 | 40 |

12 | 48 |

14 | 56 |

8 | 32 |

**Step 1: Calculate Mean of X and Y **

Mean of X ( μx ) : 10+12+14+8 / 4 = 11

Mean of Y(μy) = 40+48+56+32/4 = 44

**Step 2: Substitute the values in the formula **

xi –x̅ | yi – ȳ |

10 – 11 = -1 | 40 – 44 = – 4 |

12 – 11 = 1 | 48 – 44 = 4 |

14 – 11 = 3 | 56 – 44 = 12 |

8 – 11 = -3 | 32 – 44 = 12 |

**Substitute the above values in the formula **

Cov(x,y) = (-1) (-4) +(1)(4)+(3)(12)+(-3)(12)

___________________________

4

**Cov(x,y) =** 8/2 =** 4 **

**Hence, Co-variance for the above data is 4 **

**Step 3: Now substitute the obtained answer in Correlation formula **

Before substitution we have to find standard deviation of x and y

Lets take the data for X as mentioned in the table that is 10,12,14,8

To find standard deviation

**Step 1: Find the mean of x that is x̄**

10+14+12+8 /4 = 11

**Step 2: Find each number deviation: Subtract each score with mean to get mean deviation**

10 – 11 = -1 |

12 – 11 = 1 |

14 – 11 = 3 |

8 – 11 = -3 |

**Step 3: Square the mean deviation obtained **

-1 | 1 |

1 | 1 |

3 | 9 |

-3 | 9 |

**Step 4: Sum the squares **

1+1+9+9 = 20

**Step5: Find the variance **

**Divide the sum of squares with n-1 that is 4-1 = 3 **

20 /3 = 6.6

**Step 6: Find the square root**

Sqrt of 6.6 = 2.581

**Therefore, Standard Deviation of x = 2.581**

**Find for Y using same method **

The Standard Deviation of y = 10.29

Correlation = 4 /(**2.581** x10.29 )

Correlation = 0.15065

So, now you can understand the difference between Covariance vs Correlation.

- Covariance is used in Biology – Genetics and Molecular Biology to measure certain DNAs.
- Covariance is used in the prediction of amount investment on different assets in financial markets
- Covariance is widely used to collate data obtained from astronomical /oceanographic studies to arrive at final conclusions
- In Statistics to analyze a set of data with logical implications of principal component we can use covariance matrix
- It is also used to study signals obtained in various forms.

- Time vs Money spent by a customer on online e-commerce websites
- Comparison between the previous records of weather forecast to this current year.
- Widely used in pattern recognition
- Raise in temperature during summer v/s water consumption amongst family members is analyzed
- The relationship between population and poverty is gauged

- The graphic method
- The scatter method
- Co-relation Table
- Karl Pearson Coefficient of Correlation
- Coefficient of Concurrent deviation
- Spearman’s rank correlation coefficient

Before going into the details, let us first try to understand variance and standard deviation.

**Quick check –** Statistical Analysis Course

Variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of numbers are spread out from their average value.

Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. It essentially measures the absolute variability of a random variable.

Covariance and correlation are related to each other, in the sense that covariance determines the type of interaction between two variables, while correlation determines the direction as well as the strength of the relationship between two variables.

Both the Covariance and Correlation metrics evaluate two variables throughout the entire domain and not on a single value. The differences between them are summarized in a tabular form for quick reference. Let us look at Covariance vs Correlation.

Covariance | Correlation |

Covariance is a measure to indicate the extent to which two random variables change in tandem. | Correlation is a measure used to represent how strongly two random variables are related to each other. |

Covariance is nothing but a measure of correlation. | Correlation refers to the scaled form of covariance. |

Covariance indicates the direction of the linear relationship between variables. | Correlation on the other hand measures both the strength and direction of the linear relationship between two variables. |

Covariance can vary between -∞ and +∞ | Correlation ranges between -1 and +1 |

Covariance is affected by the change in scale. If all the values of one variable are multiplied by a constant and all the values of another variable are multiplied, by a similar or different constant, then the covariance is changed. | Correlation is not influenced by the change in scale. |

Covariance assumes the units from the product of the units of the two variables. | Correlation is dimensionless, i.e. It’s a unit-free measure of the relationship between variables. |

Covariance of two dependent variables measures how much in real quantity (i.e. cm, kg, liters) on average they co-vary. | Correlation of two dependent variables measures the proportion of how much on average these variables vary w.r.t one another. |

Covariance is zero in case of independent variables (if one variable moves and the other doesn’t) because then the variables do not necessarily move together. | Independent movements do not contribute to the total correlation. Therefore, completely independent variables have a zero correlation. |

Both Correlation and Covariance are very closely related to each other and yet they differ a lot.

When it comes to choosing between Covariance vs Correlation, the latter stands to be the first choice as it remains unaffected by the change in dimensions, location, and scale, and can also be used to make a comparison between two pairs of variables. Since it is limited to a range of -1 to +1, it is useful to draw comparisons between variables across domains. However, an important limitation is that both these concepts measure the only linear relationship.

*If you wish to learn more about statistical concepts such as covariance vs correlation, upskill with Great Learning’s **PG program in Data Science and Business Analytics.** The PGP DSBA Course is specially designed for working professionals* *and helps you power ahead in your career. You can learn with the help of mentor sessions and hands-on projects under the guidance of industry experts*. *You will also have access to career assistance and 350+ companies*. *You can also check out Great Learning Academy’s **free online certificate courses**.*

Original article source at: https://www.mygreatlearning.com

#**Covariance #Correlation **

1598839687

If you are undertaking a mobile app development for your start-up or enterprise, you are likely wondering whether to use React Native. As a popular development framework, React Native helps you to develop near-native mobile apps. However, you are probably also wondering how close you can get to a native app by using React Native. How native is React Native?

In the article, we discuss the similarities between native mobile development and development using React Native. We also touch upon where they differ and how to bridge the gaps. Read on.

Let’s briefly set the context first. We will briefly touch upon what React Native is and how it differs from earlier hybrid **frameworks**.

React Native is a popular JavaScript framework that Facebook has created. You can use this open-source framework to code natively rendering Android and iOS mobile apps. You can use it to develop web apps too.

Facebook has developed React Native based on React, its JavaScript library. The first release of React Native came in March 2015. At the time of writing this article, the latest stable release of React Native is 0.62.0, and it was released in March 2020.

Although relatively new, React Native has acquired a high degree of popularity. The “Stack Overflow Developer Survey 2019” report identifies it as the 8th most loved framework. Facebook, Walmart, and Bloomberg are some of the top companies that use React Native.

**The popularity of React Native comes from its advantages. Some of its advantages are as follows:**

- Performance: It delivers optimal performance.
- Cross-platform development: You can develop both Android and iOS apps with it. The reuse of code expedites development and reduces costs.
- UI design: React Native enables you to design simple and responsive UI for your mobile app.
- 3rd party plugins: This framework supports 3rd party plugins.
- Developer community: A vibrant community of developers support React Native.

Are you wondering whether React Native is just another of those hybrid frameworks like Ionic or Cordova? It’s not! React Native is fundamentally different from these earlier hybrid frameworks.

**React Native is very close to native. Consider the following aspects as described on the React Native website:**

- Access to many native platforms features: The primitives of React Native render to native platform UI. This means that your React Native app will use many native platform
**APIs**as native apps would do. - Near-native user experience: React Native provides several native components, and these are platform agnostic.
- The ease of accessing native APIs: React Native uses a declarative UI paradigm. This enables React Native to interact easily with native platform APIs since React Native wraps existing native code.

Due to these factors, React Native offers many more advantages compared to those earlier hybrid frameworks. We now review them.

#android app #frontend #ios app #mobile app development #benefits of react native #is react native good for mobile app development #native vs #pros and cons of react native #react mobile development #react native development #react native experience #react native framework #react native ios vs android #react native pros and cons #react native vs android #react native vs native #react native vs native performance #react vs native #why react native #why use react native

1590724123

**Correlation and Covariance** are two commonly used statistical concepts majorly used to measure the linear relation between two variables in data. When used to compare samples from different populations, covariance is used to identify how two variables vary together whereas correlation is used to determine how change in one variable is affecting the change in another variable.

#correlation vs covariance

1572701335

In this video you will learn the difference between waterfall and agile model, what is lean, lean vs agile vs waterfall differences in detail.

Why DevOps is important?

DevOps implementation is going through the roof with most of the largest software organizations around the world invested heavily in its implementation. The core values of devops is effectively based on the Agile Manifesto but with one slight change which moves the focus from creating a working software to one that is more interested in the end-to-end software service mechanism and delivery.

#agile vs waterfall vs lean #Learn Lean #What is Lean #Waterfall vs Agile #Difference Between Waterfall and Agile