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This article was published as a part of the Data Science Blogathon.

Introduction

Machine Learning is based on the idea that you receive back exactly what you put in. You will only receive trash if you offer trash. The term “trash” here refers to the noise. This is a common misunderstanding that the more features we have in our learning model, the more accurate it would be. However, this is not the scenario; not all of the features are equally important and will aid our model’s accuracy.

The number of features and model performance does not have a linear relationship, as seen in the following diagram. The model’s accuracy increases up to a certain threshold value, but after that, if we add more dimensions, the model’s accuracy will only get worse. The “Curse of Dimensionality” is the name given to this problem.

The drawbacks of adding unnecessary dimensions to data.

 It will be time-consuming. The model will take more time to get trained on the data.

The accuracy of the model may also be impacted.

The model is prone to a problem known as “Overfitting”.

Assume the two dimensions/features are strongly correlated, and that one can be found using the other one. In this case, iterating over the second feature would simply consume more time without adding improvement to the model’s accuracy.

This becomes one of the most challenging problems to deal with whenever we have a lot of features in our data. We use a technique known as “Feature Selection” to address this issue. Only the most significant features are chosen in this technique. As a consequence, accuracy may also get improved and lesser time will be consumed

Methods for Feature Selection

1) Filter Method

This approach takes all of the subsets of features and, after picking them all, attempts to determine the optimal subset of features using various statistical methods. Correlation Coefficient (Pearson, Spearman), ANOVA test, and Chi-Square test are examples of statistical techniques used.

All features that have a strong relationship with the target variable are picked. After picking the optimal subset, the machine learning algorithm is trained on it and its accuracy is evaluated.

2) Wrapper Method

It’s easier than the filter approach because statistical tests aren’t required. Wrapper methods are classified as follows:

Forward Selection: The method starts with no characteristics. Later continues to add characteristics to the model that increase its accuracy with each iteration.

Backward Selection: It starts with all the features and then eliminates those that increase the model’s accuracy in each iteration. The process will be repeated until no improvement in the elimination of any feature is detected.

Recursive Feature Elimination: This technique employs the greedy strategy. It doesn’t have all of the features. It tries to identify the most significant features. It will only accept them.

3) Embedded Method

This approach creates various subsets of features in all feasible combinations and permutations. It then chooses the subset that will provide the best accuracy.

We will learn about the ‘Boruta’ algorithm for feature selection in this article. Boruta is a Wrapper method of feature selection. It is built around the random forest algorithm. Boruta algorithm is named after a monster from Slavic folklore who resided in pine trees. 

But, exactly, how does this algorithm work? Let’s explore…

Working of Boruta

The independent variables’ shadow features are generated by Boruta. Shadow features are duplicates of the original independent features with adequate shuffling, as seen in the Figure below. This shuffle is performed to eliminate the correlation between the independent and the target attribute. Here S1, S2, and S3 are the shadow features of the original features F1, F2, and F3.

The algorithm would then merge both the original and shadow features in the second step.

Pass this combined data to the random forest algorithm. This provides the importance of the features via Mean Decrease Accuracy/Mean Decrease Impurity.

Random Forest determines the Z score for both original and shadow features based on this. Compare the shadow features’ maximum Z score to the individual original features’ Z score.

The algorithm uses the shadow features’ maximum Z score as the threshold value. The original features with a Z score higher than the max shadow feature are deemed “significant,” while those with a Z score lower than that are deemed “unimportant”.

This procedure is repeated until all the important and unimportant features have been identified, or other termination conditions have been met.

  Using R to implement Boruta

Step 1:

Load the following libraries:

library(caTools) library(Boruta) library(mlbench) library(caret) library(randomForest)

Step 2:

we will use online customer data in this example. It contains 12330 observations and 18 variables. Here the str() function is used to see the structure of the data

data <- read.csv(onlineshopping.csv, header =T) str(data)

Step 3:

Now we will use the ‘Boruta’ function to find the important and unimportant attributes. All the original features having a lesser Z score than shadow max (circled in the plot below) will be marked unimportant and after this as important.

set.seed(123) boruta_res <- Boruta(Revenue~., data= data, doTrace=2, maxRuns= 150) plot(boruta_res, las=2, cex.axis=0.8)

Step 4:

Split the data into ‘train’ & ‘test’. 75% for training and the rest 25% for testing.

set.seed(0) split <- sample.split(data,SplitRatio = 0.75) train <- subset(data,split==T) test <- subset(data,split==F)

Step 5:

Check the accuracy of the random forest model when all the features are used to train the model. Here all 17 independent features are used. It is providing an accuracy of 90.63%

rfmodel <- randomForest(Revenue ~., data = train) pred_full <- predict(rfmodel, test) confusionMatrix(table(pred_full, test$Revenue))

Step 6:

Get the formula for all the important features using the ‘getConfirmedFormula()’ function. Here 14 features are confirmed as important.

getConfirmedFormula(boruta_res)

Step 7:

Checking the accuracy of the model when trained with only important attributes. In this case, the model is giving an accuracy of 90.77% which is slightly more than the previous model even though only 14 out of 17 attributes are used.

rfmodel <- randomForest(Revenue ~ Administrative + Administrative_Duration + Informational +                        Informational_Duration + ProductRelated + ProductRelated_Duration +                        BounceRates + ExitRates + PageValues + Month + OperatingSystems +                        Browser + TrafficType + VisitorType, data = train) pred_confirmed

<- predict(rfmodel, test)

confusionMatrix(table(pred_confirmed, test$Revenue))

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Shivam Sharma & Dr Hemant Kumar Soni.

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What Is The Use Of The Address Element Type In Html?

HTML element is a section of an HTML document that tells the browser how to represent the information of that section. It contains necessary information like instructions, idea of the webpage and main content.

HTML element mainly consists of three parts −

Opening tag − An opening tag is an HTML element that begins a section of content. Opening tags tell browsers to start interpreting the content as part of a specific type of element, such as a heading or paragraph.

Closing tag − It marks the closing of the HTML element and tells the browser where it has to stop looking for content.

Content − This part contains the main information of the webpage and it lies between the opening and closing tag. Only this part of the HTML element will be visible to the user on the webpage.

Address Element

Address element in HTML is used to describe the contact information of the author or the owner of the HTML document. It contains the contact information like address, email address, phone number and social media handle etc.

It usually get placed at the top or bottom of the webpage. The content that we write in the address tag usually shows in the form of italic font in the browser, and by default web browser will add a line break before and after the address element.

An address element will do its job only if it is placed inside footer element. Earlier, we cannot use address element to show arbitrary address on our webpage but with the latest version we can now use it for arbitrary address also.

Also address element is flow content means we cannot have nested address element in HTML. At the same time address element does not allow the use of any other HTML element like article, aside, nav, heading inside it.

Example

contact us : 308, C – Wing, Suyog Co.Housing Society Ltd T. P.S. Road & III Link Road Vazira, Borivali, East Mumbai, Maharashtra, 400092 Why should we use Address Element

Whenever we specify the content in the address tag, it gets styled differently, that is somewhat similar to an italicized text. Then the question arise as why don’t we just use an italic formatting for addresses, if all it does is changing the style to italic. The answer to that is SEO.

What is SEO ?

SEO is an abbreviation for Search engine optimization. It helps in improving the website so that, whenever people search for that product or similar products, it ranks higher in the numerous results that will be displayed on the browser. This will reach the actual target audience, who will be able to see the website. It also helps in maintaining the traffic and natural search results.

Every tag in html has some form of meaning associated with it. For example, h1 tag specifies that it is a major heading and all the content within that is related to that topic. Other html tags which has special meaning are described below −

Article tag − that isolates the content from the rest of article

Section − separates group of content from other content on website

Aside − separates the content within it from the main content

Header − separates the top of the web page

Footer − can separate the bottom of the web page

Nav − it basically contains the navigation menu for the web page

Similarly an italicized formatting has completely different semantic meaning from the address tag. The address tag specifies the browser and the search engine that the content within that tag is some form of address through which we can reach out to the author or the person the article is related to.

But the italic text only mean that the author wants to emphasize that word, or group of words; but it need not to be an address. This is why the articles which use address tag are better optimized in SEO and rank higher in comparison with using italic or em tag to define address.

Example

Following is the example of displaying address using address element –

contact us : 20K, Dhakuria Station Road, Dhakuria PS: Jadavpur, Kolkata West Bengal, 700031 Conclusion

To conclude, The ADDRESS element type in HTML is a useful for providing contact information and other related details, such as physical addresses. It can also be used to provide helpful context around the content of a web page or section. With its semantic meaning and various styling possibilities, it is an essential element for any website that requires contact information or contextual support.

The Game Of Increasing R

This article was published as a part of the Data Science Blogathon.

Introduction

After building a Machine Learning model, the next and very crucial step is to evaluate the model performance on the unseen or test data and see how good our model is against a benchmark model.

The evaluation metric to be used would depend upon the type of problem you are trying to solve —whether it is a supervised, unsupervised problem, or a mix of these (like semi-supervised), and if it is a classification or a regression task.

In this article, we will discuss two important evaluation metrics used for regression problem statements and we will try to find the key difference between them and learn why these metrics are preferred over Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) for a regression problem statement.

Some Important questions which we are trying to understand in this article are as follows:

👉 The Game of increasing R-squared (R2)

👉 Why we go for adjusted-R2?

 👉 When to use which from R2 and adjusted-R2?

Let’s first understand what exactly is R Squared?

R-squared, which sometimes is also known as the coefficient of determination, defines the degree to which the variance in the dependent variable (target or response) can be explained by the independent variable (features or predictors).

Let us understand this with an example — say the R2 value for a regression model having  Income as an Independent variable (predictor) and, Expenditure as a dependent variable (response) comes out to be 0.76.

– In general terms, this means that 76% of the variation in the dependent variable is explained by the independent variables.

But for our defined regression problem statement, it can be understood as,

👉 76% variability in expenditure is associated or related with the regression equation and 24% variations are due to other factors.

👉76% variability in expenditure is explained by its linear relationship with income while 24% variations are uncounted for.

👉 76% variation in expenditure due to variation in income while we can’t say anything about the 24% variations. God knows better about it.

Image Source: link

Important points about R Squared 

👉 Ideally, we would want the independent variables to explain the complete variations in the target variable. In that scenario, the R2 value would be equal to 1. Thus we can say that the higher the R2 value, the better is our model.

👉 In simple terms, the higher the R2, the more variation is explained by your input variables, and hence better is your model. Also, the R2 would range from [0,1]. Here is the formula for calculating R2–

The R2 is calculated by dividing the sum of squares of residuals from the regression model (given by SSRES) by the total sum of squares of errors from the average model (given by SSTOT) and then subtracting it from 1.

Fig. Formula for Calculating R2

Image Source: link

Drawbacks of using R Squared :

👉 Every time if we add Xi (independent/predictor/explanatory) to a regression model, R2 increases even if the independent variable is insignificant for our regression model.

👉 R2 assumes that every independent variable in the model helps to explain variations in the dependent variable. In fact, some independent variables don’t help to explain the dependent variable. In simple words, some variables don’t contribute to predicting the dependent variable.

👉 So, if we add new features to the data (which may or may not be useful), the R2 value for the model would either increase or remain the same but it would never decrease.

So, to overcome all these problems, we have adjusted-R2 which is a slightly modified version of R2.

Let’s understand what is Adjusted R2?

👉 Similar to R2,  Adjusted-R2 measures the proportion of variations explained by only those independent variables that really help in explaining the dependent variable.

👉 Unlike R2, the Adjusted-R2 punishes for adding such independent variables that don’t help in predicting the dependent variable (target).

Let us mathematically understand how this feature is accommodated in Adjusted-R2. Here is the formula for adjusted R2

Fig. Formula for Calculating adjusted-R2

Image Source: link

Let’s take an example to understand the values changes of these metrics in a Regression model

For Example,

      Independent Variable                    R2              Adjusted-R2

                   X1                  67.8                   67.1

                   X2                  88.3                   85.6

                   X3                  92.5                   82.7

In this example for a regression problem statement, we observed that the independent variable X3 is insignificant or it doesn’t contribute to explain the variation in the dependent variable. Hence, adjusted-R2 is decreased because the involvement of in-significant variable harms the predicting power of other variables that are already included in the model and declared significant.

 R2 vs Adjusted-R2

👉 Adjusted-R2 is an improved version of R2.

👉 Adjusted-R2 includes the independent variable in the model on merit.

👉 Adjusted-R2 < R2

👉 R2 includes extraneous variations whereas adjusted-R2 includes pure variations.

👉 The difference between R2 and adjusted-R2 is only the degrees of freedom.

The Game of Increasing R2

Sometimes researchers tried their best to increase R2 in every possible way.

👉 One way to include more and more explanatory (independent) variables in the model because:

R2 is an increasing function of the number of independent variables i.e, with the inclusion of one more independent variable R2 is likely to increase or at least will not decrease.

When to use which?

Comparing models using R2

Comparing two models just based on R2 is dangerous as,

👉 Models having a different number of independent variables may have an equal value of R2.

👉 Total sample size and respective degrees of freedom are ignored.

Hence, there is a likelihood that one would choose the wrong model.

Problem solved by adjusted-R2

To compare two different models, or choose the best model, the adjusted-R2 is used because:

👉 It is adjusted for the respective degree of freedom.

👉 It takes into account the total sample size and number of independent variables.

👉 It is not an increasing function of the number of independent variables.

👉 It only increases if newly independent variables have an impact on the dependent variable.

CONCLUSION:

So, concluding the discussion we say that,

👉 R2 can be used to access the goodness of fit of a single model whereas,

👉Adjusted-R2 is used to compare two models and to see the real impact of newly added independent variables.

👉 Adjusted-R2 should be used while selecting important predictors for the regression model.

End Notes

Thanks for reading!

Please feel free to contact me on Linkedin, Email.

About the author Chirag Goyal

Currently, I am pursuing my Bachelor of Technology (B.Tech) in Computer Science and Engineering from the Indian Institute of Technology Jodhpur(IITJ). I am very enthusiastic about Machine learning, Deep Learning, and Artificial Intelligence.

The media shown in this article on Top Machine Learning Libraries in Julia are not owned by Analytics Vidhya and is used at the Author’s discretion. 

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The Secrets Of Great Teamwork

Great teamwork in an organization entails a collection of people cooperating and collaborating with one another to accomplish a common result in the end. It needs good communication, appreciation for one another, and alignment on goals. Establishing a positive work atmosphere, encouraging trust and psychological empowerment, supporting equality and diversity, and offering chances for growth both personally and professionally are all important aspects of developing a great team.

The main component of teamwork is interpersonal interaction. Whenever an individual involved can combine their particular talents and strengths in productive ways, great collaboration results.

What is Teamwork?

Teamwork is the collaborative responsibility of a group to accomplish a common objective. The magic ingredient is what elevates a team’s production above one of its individual efforts.

It might be confusing to understand where this collaboration originates from, and not each grouping manages to get along successfully. In theory, you would believe that combining two of your brightest minds will increase their productivity by double. In practice, it may double, treble, or lead to another outcome.

Benefits of Teamwork

It’s reasonable to suppose that one of your primary objectives as a leader is the profitability of your company. Obtaining that objective may be more possible with teamwork. Teams that share information more swiftly address issues. Sharing tasks among teammates helps teams operate more effectively. Teams also foster better bonds among coworkers.

Individuals are motivated to produce excellent efforts in a helpful and friendly atmosphere if they are a member of a successful team. Individuals feel encouraged to strive towards both their own ambitions and the team’s common objective. Employees function best altogether when they feel more involved in the success of the company they work for, which fosters a sense of belonging.

Characteristics of Great Teamwork

The tracking techniques are frequently present in an organization where there is strong teamwork −

Goals and clear vision − All coworkers have a common idea of the overall organizational goals and a common vision of the goals they’re striving to accomplish.

Confidence and supportiveness − Team members are free to voice their ideas and take chances without worrying about repercussions or being judged.

Accountability and responsibility − Every group member accepts ownership for the duties they are given, as well as for their contributions and accomplishments to the team.

Support for each other − Team members treat one another with regard, appreciating and appreciating each other’s distinctive talents and viewpoints.

Collaboration and cooperation − Colleagues cooperate and work together in a coordinated manner, building on each other’s skills to accomplish common objectives.

Agility and versatility − The organization is able to alter plans and tactics as necessary to meet its objectives in light of varying conditions.

Improvements − The group is dedicated to ongoing change and success, routinely evaluating their work, and looking for chances to broaden their knowledge and boost their productivity.

Unique skill − Especially when participating in a high-performance group, everyone should contribute their own background, aspirations, and specialized knowledge to the table. Individual gifts fuel overall success and solidify a group member’s position.

Feeling a part of the team − Establishing community connections and fostering a sense of confidence and order within the unit will be made easier by knowing where you belong in the larger team and how your talents connect with those of others.

Designed simply − Facilitating collaboration requires a clear structure, which is a key component. Making decisions and resolving conflicts are made easier when you are aware of the team’s structure.

Attainable targets − Unrealistic goals may be the poison of effective collaboration. People may lose interest in the task at hand if they believe failure is certain. When coworkers express their bad sentiments to each other, they can compound and harm teamwork.

Positive mindset − Positive views can rapidly saturate a team, and enthusiasm is transmittable as long as it’s not excessive. When managers and staff members care about the company’s goal and want it to flourish, great teamwork results.

Organizations that concentrate on coming up with solutions − Nobody can anticipate the future, but effective cooperation enables organizations to adjust to difficult new circumstances and to keep their attention on finding answers rather than wallowing in the issues at hand.

Ownership − The fact that the high-performing team members own the group’s objectives and are invested in the project’s success serves as their primary source of inspiration. Every group member should participate in judgment procedures. As a result, the members have aspirations and defined goals, which become the common vision. Once a common vision has been established, each team member must take responsibility for it in order to set clear goals and objectives.

The Secrets of Great Teamwork

Proper communication, a common goal, and a culture of trust, as well as a desire to work together and make concessions, are all essential building blocks of great cooperation. Having a diverse range of viewpoints and abilities in the group is also critical, as is establishing a climate in which teammates are comfortable sharing their opinions and taking chances.

Furthermore, developing a healthy team atmosphere, defining clear objectives and goals, giving feedback, and recognizing accomplishment may all contribute to the development of an exceptionally successful team.

Points to Remember for Great Teamwork

Regarding effective cooperation, keep the following in mind −

Cooperation that works requires excellent communication.

To coordinate everybody’s activities, and create a unified mission and vision.

A top team depends on mutual respect and trust.

To encourage innovative thinking, embrace variety and many viewpoints.

Establish a secure setting where team members may freely share their opinions and take chances.

Collaboration, encouragement, and acknowledgment of individual and team accomplishments will help to foster a healthy team culture.

To stop a quarrel or issue from escalating, address it as soon as possible.

For the team to continue expanding and adjusting to new challenges, promote continuous learning and growth.

Are teamwork and Collaboration the Same?

Despite their certain similarities, teamwork and collaboration are two different ideas. A collection of people working together in a planned manner to achieve a single purpose or aim is referred to as a team. It highlights the value of each member’s contributions to the overall achievement of the team.

The definition of collaborations, in contrast, is wider and stresses the sharing of information, expertise, and ideas among people and organizations in order to accomplish a common objective. Collaboration can take place between people who do not belong to the same team or organization, and it can entail a number of activities like prototyping, drawback, and information exchange.

Conclusion

In conclusion, effective cooperation is essential for the success of any business or program. It needs open communication, a common goal and goal, mutuality, trust, teamwork, flexibility, diversification, and a secure environment. Teams may establish an atmosphere that is extremely productive and productive by establishing clear aims and expectations, offering feedback and recognition, and developing a healthy team culture. To keep the team expanding and adjusting to new difficulties, teams should support constant learning and growth and address disagreements or concerns as soon as they arise.

A Fun Way To Engage Students’ Minds And Bodies With Books

Looking for a fun way to engage your students’ minds and bodies using books? That’s exactly what my colleague Jubilee Roth and I were looking for last year—a fun activity to wrap up the semester with our students—when she came across the idea of StoryWalks.

The StoryWalk Project was created by Anne Ferguson in collaboration with the Kellogg-Hubbard Library in Montpelier, Vermont. Ferguson was looking for a way to get kids and parents active together, and thus the StoryWalk was born. Since then, StoryWalks have been installed in over 300 public libraries in the United States and even worldwide in such countries as Malaysia, Russia, Pakistan, and South Korea.

Reading isn’t generally considered a dynamic activity, but students who participate in a StoryWalk get to not only hear a great story but stimulate parts of their brain that are normally at rest when they sit down with a book. Instead of snuggling up in a cozy reading spot, readers are presented with colorful pages from an illustrated book, displayed one-by-one on stakes as they stroll along an indoor or outdoor walking path. Readers are able to take their time and reflect on the subtle nuances of the story, make inferences about what may happen next, and have co-constructed conversations with any walking partners.

How to Set Up a StoryWalk

You’ll need two copies of whatever book you choose because the pages of most illustrated books are double-sided. After taking the books apart, laminate them and mount them. Make sure you get stakes that are high enough that the pages can be read without crouching down, then place them at a relaxed distance from each other along the path of your choosing.

It’s really important to consider where you place your StoryWalk path. I did not take into consideration, for example, the closeness of my StoryWalk to our third-grade portable classrooms, which had the windows open because it was warm. Not only was the StoryWalk disruptive to that classroom, but all of the third-grade students knew the ending of the story.

Choosing Books for a StoryWalk

The right book at the right time can make all the difference. Since books bridge the gap between what readers know and what they have yet to experience, careful book selection can make StoryWalks even more powerful. Here are some things to keep in mind:

Picture books are ideal for this activity because they’re short and captivating.

Social and emotional learning can be supported with illustrated books that include themes like self-awareness, self-management, self-efficacy, and social awareness.

It’s important to keep readers interested so that they continue to the end of the path. Try choosing a book with a surprise ending and keep them guessing!

It helps to choose a book with readability and possible relevance to the community.

Here are some of the books I chose:

Baghead, written and illustrated by Jarrett J. Krosoczka

Weezer Changes the World, written and illustrated by David McPhail

One Cool Friend, written by Toni Buzzeo, illustrated by David Small

Sheep Take a Hike, written by Nancy Shaw, illustrated by Margot Apple

Although we tend to think of fiction when choosing books for a StoryWalk, nonfiction can also be effective. Imagine learning the parts of a cell as you walk between pages or reading a how-to instructional story or the biography of a prominent historical figure.

Behavior During a StoryWalk

Managing behavior during a StoryWalk can be a bit tricky if you don’t provide students with some expectations ahead of time. Much like a field trip, StoryWalks involve a lot of space sharing, which requires a different set of social norms. I found that younger students especially were not accustomed to traveling in a large group.

Explain to students how to ensure that everyone has a view of the pages as you walk. The front row will need to crouch down so the back row can see. Students need to form a half-circle around each page. You can, of course, arrange your StoryWalkers into multiple smaller groups as opposed to an entire class, which could make it easier.

It is also important to show students how to walk and talk about the story, so they are not just quickly walking through the StoryWalk, missing the benefit of reading together in this way. Have students raise their hands to read a page aloud. Ask stimulating questions between pages to help them relate the story to their own experiences, further drawing them in. Encourage students to take their time and interact with each other, sharing their thoughts about the story and characters.

Extension Activities

After completing a StoryWalk, extension activities can provide a deeper understanding for students as well as keep the conversation—and therefore the learning—going.

Students can try to write an alternate ending or even add to the story’s original ending. Our youngest students can draw their responses to these prompts, while we transcribe the words to go with them. Older students can do peer reviews, co-write responses, or illustrate them and even use media to animate.

Invite students to share about a time when they did something that was featured in the story. Before we did our StoryWalk for the book Baghead, I held up a paper bag that I had cut holes out of to make a face. I asked students, “Why would someone wear this?” Students wrote down their predictions. After our StoryWalk, they came back to their predictions to write about what came true or didn’t, and any surprises in the story. Some chose to write about a time when they tried to cut their own hair, as the protagonist had, and what happened next.

How To Find The Length Of Sequence Vector In R?

A sequence vector is created by using the sequence of numbers such as 1 to 15, 21 to 51, 101 to 150, -5 to 10. The length of this type of vectors can be found only by using the length function.

For example, if we have a sequence vector say X then the length of X can be found by using the command given below −

length(X) Example 1

To find the length of sequence vector in R, use the code given below −

x1<-c(1:51,57:200,201:213) x1 Output

If you execute the above given code, it generates the following output −

[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 57 58 59 [55] 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 [73] 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 [91] 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 [109] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 [127] 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 [145] 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 [163] 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 [181] 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 [199] 204 205 206 207 208 209 210 211 212 213

To find the length of sequence vector in R, add the following code to the above code −

x1<-c(1:51,57:200,201:213) length(x1) Output

If you execute all the above given codes as a single program, it generates the following output −

[1] 208 Example 2

To find the length of sequence vector in R, use the code given below −

x2<-c(14:-50,7:48,23:98,21:-10) x2 Output

If you execute the above given code, it generates the following output −

[1] 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 [19] -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 [37] -22 -23 -24 -25 -26 -27 -28 -29 -30 -31 -32 -33 -34 -35 -36 -37 -38 -39 [55] -40 -41 -42 -43 -44 -45 -46 -47 -48 -49 -50 7 8 9 10 11 12 13 [73] 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 [91] 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 23 [109] 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 [127] 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 [145] 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 [163] 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 [181] 96 97 98 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 [199] 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

To find the length of sequence vector in R, add the following code to the above code −

x2<-c(14:-50,7:48,23:98,21:-10) length(x2) Output

If you execute all the above given codes as a single program, it generates the following output −

[1] 215 Example 3

To find the length of sequence vector in R, use the code given below −

x3<-c(25:-100,1:78,35:-10,40:-5) x3 Output

If you execute the above given code, it generates the following output −

[1] 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 [16] 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 [31] -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 [46] -20 -21 -22 -23 -24 -25 -26 -27 -28 -29 -30 -31 -32 -33 -34 [61] -35 -36 -37 -38 -39 -40 -41 -42 -43 -44 -45 -46 -47 -48 -49 [76] -50 -51 -52 -53 -54 -55 -56 -57 -58 -59 -60 -61 -62 -63 -64 [91] -65 -66 -67 -68 -69 -70 -71 -72 -73 -74 -75 -76 -77 -78 -79 [106] -80 -81 -82 -83 -84 -85 -86 -87 -88 -89 -90 -91 -92 -93 -94 [121] -95 -96 -97 -98 -99 -100 1 2 3 4 5 6 7 8 9 [136] 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 [151] 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 [166] 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 [181] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 [196] 70 71 72 73 74 75 76 77 78 35 34 33 32 31 30 [211] 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 [226] 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 [241] -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 40 39 38 37 36 [256] 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 [271] 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 [286] 5 4 3 2 1 0 -1 -2 -3 -4 -5

To find the length of sequence vector in R, add the following code to the above code −

x3<-c(25:-100,1:78,35:-10,40:-5) length(x3) Output

If you execute all the above given codes as a single program, it generates the following output −

[1] 296 Example 4

To find the length of sequence vector in R, use the code given below −

x4<-c(-50:25,5:61,69:151) x4 Output

If you execute the above given code, it generates the following output −

[1] -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 [19] -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 [37] -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 [55] 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 [73] 22 23 24 25 5 6 7 8 9 10 11 12 13 14 15 16 17 18 [91] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 [109] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 [127] 55 56 57 58 59 60 61 69 70 71 72 73 74 75 76 77 78 79 [145] 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 [163] 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 [181] 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 [199] 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151

To find the length of sequence vector in R, add the following code to the above code −

x4<-c(-50:25,5:61,69:151) length(x4) Output

If you execute all the above given codes as a single program, it generates the following output −

[1] 216 Example 5

To find the length of sequence vector in R, use the code given below −

x5<-c(-5:100,9:79,21:-21) x5 Output

If you execute the above given code, it generates the following output −

[1] -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 [19] 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 [37] 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 [55] 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 [73] 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 [91] 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 9 10 [109] 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 [127] 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 [145] 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 [163] 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 21 20 19 [181] 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 [199] 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 [217] -18 -19 -20 -21

To find the length of sequence vector in R, add the following code to the above code −

x5<-c(-5:100,9:79,21:-21) length(x5) Output

If you execute all the above given codes as a single program, it generates the following output −

[1] 220

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