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Overview of Simple Linear Regression in R

The relationship is established in the form of a mathematical equation obtained through various values of the two variables through complex calculations. Just establishing a relationship is not enough, but data must also meet certain assumptions. R programming offers an effective and robust mechanism to implement the concept.

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Advantages of Simple Linear Regression in R

Advantages of using Linear Regression Model:

Robust statistical model.

Helps us to make forecast and prediction.

It helps us to make better business decisions.

It helps us to take a rational call on the logical front.

We can take corrective actions for the errors left out in this model.

Equation of Linear regression model

The Equation of Linear regression model is given below:

Y = β1 + β2X + ϵ

Independent Variable is X

Dependent Variable is Y

β1 is an intercept of the regression model

β2 is a slope of the regression model

ϵ is the error term

We will work on the “cars” dataset which comes inbuilt with Rstudio.

Let see how the structure of the cars dataset looks like.

For this, we will use the Str() code.

str(cars)

Here we can see that our dataset contains two variables Speed and Distance.

Speed is an independent variable and Distance is a dependent variable.

Let’s take the statistical view of the cars dataset.

For this, we will use the Summary() code.

summary(cars)

In speed variable we have maximum observation is 25 whereas in distance variable the maximum observation is 120. Similarly, minimum observation in speed is 4 and distance is 2.

The Plot Visualization

To understand more about data we will use some visualization:

A scatter plot: Helps to identify whether there is any type of correlation is present between the two variables.

Box plot: Helps us to display the distribution of data. Distribution of data based on minimum, first quartile, median, third quartile and maximum.

The density plot: Helps us to show the probability density function graphically.

1. Scatter plot

It will help to visualize any relationships between the X variable and the Y variable.

#Scatterplotscatter.smooth(x=cars\$speed, y=cars\$dist, main="Dist ~ Speed", xlab = "Speed", ylab = "Distance" )

2. Box Plot

Box plot helps us to identify the outliers in both X and Y variables if any.

Code for box plot looks like this:

boxplot.stats(cars\$speed)\$out))

3. Density Plot

This plot helps to see the normality of the distribution

polygon(density(cars\$dist), col=”red”)

Types of Correlation Analysis

This analysis helps us to find the relationship between the variables.

Types of correlation analysis:

Weak Correlation (a value closer to 0)

Strong Correlation (a value closer to ± 0.99)

Perfect Correlation

No Correlation

Negative Correlation (-0.99 to -0.01)

Positive Correlation (0.01 to 0.99)

cor(cars\$speed, cars\$dist)

0.8068949 signifies that there is a strong positive correlation between the two variables (Speed and Distance).

Linear Regression model

Now we will start the most important part of the model.

The formula used for linear regression is lm(Dependent Variable ~ Independent Variable)

print(linear_regression)

We will fit these output in our regression analysis equation

Y = β1 + β2X + ϵ

dist = −17.579 + 3.932∗speed

To get a summary of the linear regression model, we will use code Summary()

summary(linear_regression)

Now we will understand what these outcomes mean.

R squared (R2) also known as the coefficient of determination. It will tell us what proportion of change in the dependent variable caused by the independent variable. It is always between 0 and 1. The higher the value of the R squared the better the model is.

Adjusted R Squared, it is a better statistic to consider if we want to see the credibility of our model. Adjusted R2 helps us to check the goodness of the model also and it will also penalize the model if we add a variable that does not improve our existing model.

As per our model summary, Adjusted R squared is 0.6438 or we can say that 64% of the variance in the data is being explained by the model.

Further, there are many statistics to check the credibility of our model like t-statistic, F-statistic, etc.

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## Python Polynomial Regression In Machine Learning

Introduction

The link between the dependent and independent variables, Y and X, is modelled as the nth degree of the polynomial in polynomial regression, a type of linear regression. In order to draw the best line using data points, this is done. Let’s explore more about the Polynomial regression in this article.

Polynomial Regression

One of the rare instances of multiple linear regression models is polynomial regression. In other words, it is a sort of linear regression when the dependent and independent variables have a curvilinear connection to one another. In the data, a polynomial connection is fitted.

Additionally, by incorporating several polynomial parts, a number of linear regression equations are transformed into polynomial regression equations.

Need of Polynomial Regression

A few criteria that specify the requirement for polynomial regression are listed below.

If a linear model is used to a linear database, as is the case with simple linear regression, a good result is produced. However, a significant output is calculated if this model is applied to a non-linear dataset with no adjustments. These result in increased mistake rates, a drop in accuracy, and an increase inside the loss function.

Polynomial regression is required in situations when the data points are organized non-linearly.

A linear model won’t cover any data points if a non-linear model is available and we attempt to cover it. In order to guarantee that all of the data points are covered, a polynomial model is employed. Nevertheless, a curve rather than a straight line will work well for most data points when employing polynomial models.

A scatter diagram of residuals (Y-axis) here on predictor (X-axis) will show regions of many positive residuals inside the middle if we attempt to fit a linear model to curved data. As a result, it is inappropriate in this circumstance.

Polynomial Regression Applications

Basically, these are employed to define or enumerate non-linear phenomena.

The rate of tissue growth.

Progression of pandemic disease.

Carbon isotope distribution in lake sediments.

Modeling the estimated return of a dependent variable y in relation to the value of an independent variable x is the fundamental aim of regression analysis. We used the equation below in simple regression

y = a + bx + e

Here, the dependent variable is y, along with the independent variables a, b, and e.

Polynomial Regression Types

Numerous varieties of polynomial regression exist since a polynomial equation’s degree has no upper bound and can go up to the nth number. For instance, the second degree of a polynomial equation is typically expressed as a quadratic equation when spoken. As indicated, this degree is valid up to the nth number, and we are free to deduce quite so many equations as we require or want. As a result, polynomial regression is typically categorized as follows.

When the degree is 1, linear.

Equation has a quadratic degree of two.

Depending on the degree used, cubic with a degree as three continues.

When examining the output of chemical synthesis in terms of the temperature where the synthesis takes place, for instance, this linear model will frequently not work out. In such circumstances, we employ a quadratic model.

y = a+b1x+b2+b2+e

Here, the error rate is e, the y-intercept is a, and y is the dependent variable on x.

Python Implementation of Polynomial Regression

Step 1 − Import datasets and libraries

Import the necessary libraries as well as the dataset for the polynomial regression analysis.

# Importing up the libraries import numpy as nm import matplotlib.pyplot as mplt import pandas as ps # Importing up the dataset data = ps.read_csv('data.csv') data

Output sno Temperature Pressure 0 1 0 0.0002 1 2 20 0.0012 2 3 40 0.0060 3 4 60 0.0300 4 5 80 0.0900 5 6 100 0.2700

Step 2 − The dataset is split into two components in step two.

Divide the dataset into the X and y components. X will contain the columns 1 and 2. The two columns will be in column y.

X = data.iloc[:, 1:2].values y = data.iloc[:, 2].values

Step 3 − Dataset fitting with linear regression

Two components of the linear regression model are fitted.

from sklearn.linear_model import LinearRegressiondata line2 = LinearRegressiondata() line2.fit(X, y)

Step 4 − Polynomial Regression Fitting to the Dataset

X and Y are the two components to which the polynomial regression model is fit.

from sklearn.preprocessing import PolynomialFeaturesdata poly = PolynomialFeaturesdata(degree = 4) X_polyn = polyn.fit_transform(X) polyn.fit(X_polyn, y) line3 = LinearRegressiondata() line3.fit(X_polyn, y)

Step 5 − In this stage, we are utilizing a scatter plot to visualize the results of the linear regression.

mplt.scatter(X, y, color = 'blue') mplt.plot(X, lin.predict(X), color = 'red') mplt.title('Linear Regression') mplt.xlabel('Temperature') mplt.ylabel('Pressure') mplt.show()

Output

Step 6 − Using a scatter plot to display the polynomial regression findings.

mplt.scatter(X, y, color = 'blue') mplt.plot(X, lin2.predict(polyn.fit_transform(X)), color = 'red') mplt.title('Polynomial Regression') mplt.xlabel('Temperature') mplt.ylabel('Pressure') mplt.show()

Output

Step 7 − Use both linear & polynomial regression to forecast future outcomes. A NumPy 2D array must contain the input variable, it should be noted.

Linear Regression

predic = 110.0 predicdarray = nm.array([[predic]]) line2.predict(predicdarray)

Output Array([0.20657625]) Polynomial Regression

Predic2 = 110.0 predic2array = nm.array([[predic2]]) line3.predicdict(polyn.fit_transform(predicd2array))

It is capable of doing a wide variety of tasks.

In general, polynomial suits a large range of curved surfaces.

The closest representation of the relationship between variables is provided by polynomials.

These are extremely responsive to deviations.

The outcomes of a nonlinear analysis might be significantly impacted by the existence of one or two variables.

Additionally, compared to linear regression, there are unfortunately less model validation techniques available for the discovery of deviations in nonlinear regression.

Conclusion

We have learned the theory underlying polynomial regression in this article. We learned the implementation of the Polynomial regression.

After applying this model to a real dataset, we could see its graph and utilize it to predict things. We hope this session was beneficial and that we can now confidently apply this knowledge to other datasets.

## How To Change The Name Of Variables In A List In R?

The name of variables in a list are actually the list elements. These elements can be either named or unnamed. The naming can be done with the help of names function and renaming can be done in the same way as well. For example, if we have a list called LIST then the names of the element in LIST can be done by using the below command: names(LIST)<−c(“New_name1″,” New_name2″,” New_name3″)

Example1

Live Demo

List1<−list(x1=rnorm(50),x2=rnorm(50),x3=rnorm(50),x4=rnorm(50)) List1 Output \$x1  0.22045578 0.87621081 −2.14896295 −0.23375135 −1.99849285 −1.23478040  0.84630372 −0.04649482 0.40364277 0.76745466 0.86710150 −1.25458115  −0.15779799 −0.51231678 0.41302087 0.56425626 0.72606595 −0.41510222  0.04161530 0.22429205 0.78640914 −0.42336284 −0.36753396 −1.76702031  −0.18353788 0.83487200 −0.58720051 −0.35893240 2.11412884 0.64541105  −0.31231996 1.18544828 0.55379896 −0.05375394 2.12746303 −0.18770648  0.09875784 1.91037815 1.62145572 2.09306799 −0.69223593 −2.28719811  −1.65560167 0.56950942 −0.47122259 −0.03320968 0.37736707 1.15771800  1.39865000 2.11850393 \$x2  −1.08745987 1.21603339 0.67722530 −0.72637691 0.11284394 0.06521357  −0.63062721 0.51885546 −0.80294450 −0.68162320 −0.03716272 −0.28727432  −1.02602717 1.39835918 0.83669025 −0.32989626 0.53480226 −1.20725319  0.62876732 0.57616473 1.23622388 0.47553964 −1.54714749 0.05546880  0.68006209 −1.35020237 0.24510244 −0.30734854 0.73136457 0.20138181  −1.57546283 0.02353878 0.80164111 −2.55562737 −0.52691068 −1.31285889  0.80086135 0.71310077 1.03191486 1.68180850 −0.22631040 −0.19792903  1.04370225 −0.44173735 −1.63662910 0.21156259 −0.46483173 −0.66235721  −0.13295360 −1.32170171 \$x3  0.07669278 −0.38499088 0.94730644 0.02168627 −0.45829401 0.22886214  −1.39640763 0.92429420 0.06621604 0.80289084 −0.06052526 0.08932862  0.40131138 −0.88856060 1.44916943 0.20551047 −0.05611997 −0.63985946  0.71778100 −0.06450029 0.13242960 0.03471508 0.28165263 0.91927825  −1.04272315 −0.21362268 1.77794708 1.46094086 −0.36455082 −0.61316042  0.49590678 0.24563859 −0.12790481 −1.25043942 1.63435096 0.97543576  1.08407794 −0.35938727 −1.01551967 1.33552147 −0.15556228 0.92660850  0.88924569 0.14511699 −0.81864663 −1.23682286 2.31722565 0.05072431  0.29083551 −1.81128974 \$x4  −1.14514769 1.28087282 −1.35947002 1.88497074 −1.36860156 0.54394041  −1.23803017 1.87713234 −1.44581007 −0.15336740 −0.94568862 0.31240499  0.27472438 −0.31544232 −0.38436760 −1.42893573 0.96341769 0.61378162  −0.36855443 −1.80704466 1.35543844 0.44568017 0.16479479 0.02997777  −0.67611291 1.13604965 2.16933213 −1.08901929 −1.10272610 1.30263617  −2.77832551 0.34131156 −0.22354979 −0.19877160 1.63330268 −1.86962151  −0.25008885 −1.37075933 1.45126184 −2.13790977 −0.57726105 0.23644945  1.09985656 0.56128271 2.30362701 2.02089590 −0.05787852 0.44209338  −1.30333114 −0.03522043 Example names(List1)<−c("Norm_default1","Norm_default2","Norm_default3","Norm_default4") List1 Output \$Norm_default1  0.22045578 0.87621081 −2.14896295 −0.23375135 −1.99849285 −1.23478040  0.84630372 −0.04649482 0.40364277 0.76745466 0.86710150 −1.25458115  −0.15779799 −0.51231678 0.41302087 0.56425626 0.72606595 −0.41510222  0.04161530 0.22429205 0.78640914 −0.42336284 −0.36753396 −1.76702031  −0.18353788 0.83487200 −0.58720051 −0.35893240 2.11412884 0.64541105  −0.31231996 1.18544828 0.55379896 −0.05375394 2.12746303 −0.18770648  0.09875784 1.91037815 1.62145572 2.09306799 −0.69223593 −2.28719811  −1.65560167 0.56950942 −0.47122259 −0.03320968 0.37736707 1.15771800  1.39865000 2.11850393 \$Norm_default2  −1.08745987 1.21603339 0.67722530 −0.72637691 0.11284394 0.06521357  −0.63062721 0.51885546 −0.80294450 −0.68162320 −0.03716272 −0.28727432  −1.02602717 1.39835918 0.83669025 −0.32989626 0.53480226 −1.20725319  0.62876732 0.57616473 1.23622388 0.47553964 −1.54714749 0.05546880  0.68006209 −1.35020237 0.24510244 −0.30734854 0.73136457 0.20138181  −1.57546283 0.02353878 0.80164111 −2.55562737 −0.52691068 −1.31285889  0.80086135 0.71310077 1.03191486 1.68180850 −0.22631040 −0.19792903  1.04370225 −0.44173735 −1.63662910 0.21156259 −0.46483173 −0.66235721  −0.13295360 −1.32170171 \$Norm_default3  0.07669278 −0.38499088 0.94730644 0.02168627 −0.45829401 0.22886214  −1.39640763 0.92429420 0.06621604 0.80289084 −0.06052526 0.08932862  0.40131138 −0.88856060 1.44916943 0.20551047 −0.05611997 −0.63985946  0.71778100 −0.06450029 0.13242960 0.03471508 0.28165263 0.91927825  −1.04272315 −0.21362268 1.77794708 1.46094086 −0.36455082 −0.61316042  0.49590678 0.24563859 −0.12790481 −1.25043942 1.63435096 0.97543576  1.08407794 −0.35938727 −1.01551967 1.33552147 −0.15556228 0.92660850  0.88924569 0.14511699 −0.81864663 −1.23682286 2.31722565 0.05072431  0.29083551 −1.81128974 \$Norm_default4  −1.14514769 1.28087282 −1.35947002 1.88497074 −1.36860156 0.54394041  −1.23803017 1.87713234 −1.44581007 −0.15336740 −0.94568862 0.31240499  0.27472438 −0.31544232 −0.38436760 −1.42893573 0.96341769 0.61378162  −0.36855443 −1.80704466 1.35543844 0.44568017 0.16479479 0.02997777  −0.67611291 1.13604965 2.16933213 −1.08901929 −1.10272610 1.30263617  −2.77832551 0.34131156 −0.22354979 −0.19877160 1.63330268 −1.86962151  −0.25008885 −1.37075933 1.45126184 −2.13790977 −0.57726105 0.23644945  1.09985656 0.56128271 2.30362701 2.02089590 −0.05787852 0.44209338  −1.30333114 −0.03522043 Example2

Live Demo

List2<−list(y1<−rpois(100,5),y2=rpois(100,5),y3=rpois(100,5),y4=rpois(100,5),y5=rpois(100,5)) List2 Output []  6 6 4 6 8 8 3 4 6 4 6 6 6 1 2 3 2 6 3 5 3 8 3 10 5  4 5 7 2 1 7 2 7 0 5 7 7 5 10 5 7 4 4 3 4 2 7 6 3 4  10 4 5 5 2 3 5 7 7 5 4 1 3 5 4 4 2 4 5 7 4 2 5 9 6  5 4 4 8 6 3 2 4 6 2 2 5 4 7 5 6 2 8 6 5 5 5 7 8 6 \$y2  4 5 3 5 4 6 8 6 5 4 6 3 3 3 3 5 3 6 4 11 7 7 6 8 5  1 6 6 1 9 3 3 4 6 8 7 3 5 1 2 3 5 7 3 1 3 7 4 5 3  5 5 7 9 11 3 5 4 6 4 2 6 4 3 7 7 1 6 3 4 9 6 6 4 6  3 4 8 8 3 3 4 1 7 7 5 1 5 2 3 4 6 3 3 3 5 4 6 8 4 \$y3  4 5 0 4 9 3 7 1 5 3 0 5 8 4 3 8 9 3 7 3 6 6 5 10 9  6 2 5 3 6 5 3 6 5 6 4 6 2 5 5 2 6 2 6 4 4 7 5 5 5  5 5 3 7 6 5 3 4 1 7 8 7 5 2 2 5 6 3 5 5 5 9 3 8 5  6 4 4 4 4 1 5 5 5 4 6 6 5 5 3 2 8 2 5 5 5 3 9 2 2 \$y4  4 3 3 7 3 8 5 2 4 2 0 4 7 7 8 11 8 8 1 5 4 3 8 6 5  5 7 10 2 4 5 5 6 4 8 5 8 9 5 6 4 4 2 7 5 2 7 3 3 3  4 3 5 5 6 8 2 6 6 2 4 1 5 1 5 6 2 1 3 2 5 5 6 4 7  4 3 6 4 3 3 3 3 7 3 7 3 4 3 7 7 5 8 3 8 8 8 3 5 6 \$y5  6 7 5 3 5 6 3 6 8 5 4 8 3 2 4 3 5 4 2 1 9 6 14 4 8  2 8 3 5 5 8 10 4 3 7 4 6 4 2 4 8 10 3 4 4 7 7 8 7 6  3 6 6 7 5 6 3 8 0 7 5 6 3 3 5 1 5 2 7 7 5 5 3 12 5  9 4 7 4 6 5 6 5 5 8 5 3 1 8 3 9 3 3 6 4 8 3 3 6 6 Example names(List2)<−c("Pois1","Pois2","Pois3","Pois4","Pois5") List2 Output \$Pois1  6 6 4 6 8 8 3 4 6 4 6 6 6 1 2 3 2 6 3 5 3 8 3 10 5  4 5 7 2 1 7 2 7 0 5 7 7 5 10 5 7 4 4 3 4 2 7 6 3 4  10 4 5 5 2 3 5 7 7 5 4 1 3 5 4 4 2 4 5 7 4 2 5 9 6  5 4 4 8 6 3 2 4 6 2 2 5 4 7 5 6 2 8 6 5 5 5 7 8 6 \$Pois2  4 5 3 5 4 6 8 6 5 4 6 3 3 3 3 5 3 6 4 11 7 7 6 8 5  1 6 6 1 9 3 3 4 6 8 7 3 5 1 2 3 5 7 3 1 3 7 4 5 3  5 5 7 9 11 3 5 4 6 4 2 6 4 3 7 7 1 6 3 4 9 6 6 4 6  3 4 8 8 3 3 4 1 7 7 5 1 5 2 3 4 6 3 3 3 5 4 6 8 4 \$Pois3  4 5 0 4 9 3 7 1 5 3 0 5 8 4 3 8 9 3 7 3 6 6 5 10 9  6 2 5 3 6 5 3 6 5 6 4 6 2 5 5 2 6 2 6 4 4 7 5 5 5  5 5 3 7 6 5 3 4 1 7 8 7 5 2 2 5 6 3 5 5 5 9 3 8 5  6 4 4 4 4 1 5 5 5 4 6 6 5 5 3 2 8 2 5 5 5 3 9 2 2 \$Pois4  4 3 3 7 3 8 5 2 4 2 0 4 7 7 8 11 8 8 1 5 4 3 8 6 5  5 7 10 2 4 5 5 6 4 8 5 8 9 5 6 4 4 2 7 5 2 7 3 3 3  4 3 5 5 6 8 2 6 6 2 4 1 5 1 5 6 2 1 3 2 5 5 6 4 7  4 3 6 4 3 3 3 3 7 3 7 3 4 3 7 7 5 8 3 8 8 8 3 5 6 \$Pois5  6 7 5 3 5 6 3 6 8 5 4 8 3 2 4 3 5 4 2 1 9 6 14 4 8  2 8 3 5 5 8 10 4 3 7 4 6 4 2 4 8 10 3 4 4 7 7 8 7 6  3 6 6 7 5 6 3 8 0 7 5 6 3 3 5 1 5 2 7 7 5 5 3 12 5  9 4 7 4 6 5 6 5 5 8 5 3 1 8 3 9 3 3 6 4 8 3 3 6 6

## The Seq() Function In R: A Complete Guide (With Examples)

Dealing with number sequences in data science is common. Having the tools to easily produce sequences of numbers of different lengths, stepsizes, and start/end values is crucial. This way you can avoid having to write loops to produce number sequences over and over again. In R, you can use the built-in seq() function to create number sequences easily.

x <- seq(10) # 1,2,3,4,5,6,7,8,9,10

This is a comprehensive guide to the seq() function in R.

You will learn the syntax among the different optional parameters. All the theory is backed up by great and illustrative examples that cover each of the seq() function parameters.

What Is the seq() Function in R?

In R, you can generate a sequence of numbers with the built-in seq() function. The seq() function allows you to control the start and end values of the sequence as well as the desired length and step size.

Before taking a look at examples, let’s see what the complete syntax of the seq() function looks like.

Syntax

Typically, you see the seq() function being used with a single argument like this:

x <- seq(10)

This produces a sequence of numbers from 1 to 10.

But the full syntax of the seq() function in R is:

seq(from=1, to=1, by=1, length.out=NULL, along.with=NULL)

Where:

from is the starting value of the sequence.

to is the end value of the sequence.

by is the “jump length” by which the values are incremented every step.

chúng tôi is the desired sequence length.

along.with is the desired sequence length that matches the length of another data object.

In the examples section, you will learn how to use each of these parameters in the seq() function call.

Examples of the seq() Function in R

Let’s take a look at 5 different examples of the seq() function in R that covers all the different parameters.

Example 1: The ‘from’ Parameter

The most basic way to call the seq() function in R is by giving it a single parameter, that is, the end value of the sequence. When you do this, the default start value of the sequence is 1 as well as the default step size.

For example, let’s create a sequence of numbers from 1 to 10:

x <- seq(10) x

Output:

 1 2 3 4 5 6 7 8 9 10 Example 2: The ‘from’ and ‘to’ Parameters

Not always do you want the sequence to start from 1. In this case, you can specify both the start and the end values for the sequence by specifying the from and to parameters in the seq() function call.

For example, let’s produce a sequence of numbers from 5 to 10:

x <- seq(from=5, to=10) x

Output:

 5 6 7 8 9 10 Example 3: The ‘by’ Parameter

Thus far you’ve seen examples where the stepsize is 1, that is, consecutive numbers are incremented by 1 in the sequence. But if you want to produce sequences with stepsizes other than 1, you need to specify the optional by argument in the seq() call.

For example, let’s create a sequence of numbers from 5 to 100 with a stepsize of 10:

x <- seq(from=5, to=100, by=10) x

Output:

 5 15 25 35 45 55 65 75 85 95 Example 4: The ‘length.out’ Parameter

Sometimes it’s useful to specify a sequence of numbers in a range with a fixed length. This way you can uniformly distribute values of a certain length to a sequence of predetermined length.

For example, let’s generate a sequence of values between 0 and 10 and set the desired length of the sequence at 4:

x <- seq(from=0, to=10, length.out=4) x

Output:

 0.000000 3.333333 6.666667 10.000000

The seq() function calculates the numbers such that they are evenly distributed across the range.

Example 5: The ‘along.with’ Parameter

When dealing with multiple sequences of numbers, you sometimes might want to generate a new sequence such that it matches the length of another one.

Of course, you could set the optional out.length variable to the length of the desired sequence. But if the length needs to match with another sequence, it’s safer to specify the optional along.with parameter. This way the code is more consistent and the intent is clearer.

For example:

y <- c(0.1, 1.5, 2.9, 4.6) x <- seq(from=0, to=10, along.with=y) x

Output:

 0.000000 3.333333 6.666667 10.000000 Summary

Today you learned how to use the built-in seq() function in R.

To recap, the seq() function produces a sequence of numbers from a start value to the end. You can use the seq() function to produce sequences with the desired length, stepsize, and start/end values.

## How To Merge Two Matrices By Combining Rows In R?

By combining rows means that we want to concatenate rows of matrices but create separate columns as in the original matrices. For example, if we have two matrices say M1 and M2 as shown below −

M1 1 2 3 3 2 1 M2 2 3 5 1 2 3

Then merging of these two matrices by combining rows will result in −

1 2 3 2 3 5 > M1 Output       [,1] [,2] [1,]  5     2 [2,]  7     4 [3,]  3     6 [4,]  7     7 [5,]  5     3 [6,]  2     7 [7,]  4     7 [8,]  10    7 [9,]  7     2 [10,] 2     4 [11,] 7     5 [12,] 1     6 [13,] 2     3 [14,] 4     6 [15,] 7     6 [16,] 5     7 [17,] 3     2 [18,] 7     4 [19,] 9     6 > M2 Output      [,1] [,2] [1,]  4    7 [2,]  2    9 [3,]  5    3 [4,]  2    10 [5,]  5    2 [6,]  5    5 [7,]  3    7 [8,]  6    5 [9,]  4    4 [10,] 5    0 [11,] 3    3 [12,] 5    2 [13,] 3    8 [14,] 2    6 [15,] 2    4 [16,] 10   5 [17,] 5    8 [18,] 1    4 [19,] 6    6 1  1         5    2    4    7 2  10        2    4    5    0 3  11        7    5    3    3 4  12        1    6    5    2 5  13        2    3    3    8 6  14        4    6    2    6 7  15        7    6    2    4 8  16        5    7    10   5 9  17        3    2    5    8 10 18        7    4    1    4 11 19        9    6    6    6 12 2         7    4    2    9 13 20        5    6    4    6 14 3         3    6    5    3 15 4         7    7    2    10 16 5         5    3    5    2 17 6         2    7    5    5 18 7         4    7    3    7 19 8         10   7    6    5 > M3 Output      [,1] [,2] [1,]  0   1 [2,]  0   1 [3,]  3   0 [4,]  2   0 [5,]  0   1 [6,]  2   1 [7,]  1   0 [8,]  2   0 [9,]  2   1 [10,] 0   1 [11,] 3   0 [12,] 2   0 [13,] 2   0 [14,] 1   2 [15,] 1   2 [16,] 0   1 [17,] 4   1 [18,] 1   1 [19,] 1   2 > M4 Output      [,1] [,2] [1,]  1    0 [2,]  2    2 [3,]  1    0 [4,]  1    0 [5,]  0    2 [6,]  1    1 [7,]  2    0 [8,]  2    1 [9,]  0    0 [10,] 0    1 [11,] 3    0 [12,] 3    2 [13,] 3    5 [14,] 0    0 [15,] 2    1 [16,] 0    0 [17,] 1    1 [18,] 0    0 [19,] 1    1 1  1         0    1    1    0 2  10        0    1    0    1 3  11        3    0    3    0 4  12        2    0    3    2 5  13        2    0    3    5 6  14        1    2    0    0 7  15        1    2    2    1 8  16        0    1    0    0 9  17        4    1    1    1 10 18        1    1    0 0 11 19        1    2    1 1 12 2         0    1    2 2 13 20        1    1    1 2 14 3         3    0    1 0 15 4         2    0    1 0 16 5         0    1    0 2 17 6         2    1    1 1 18 7         1    0    2 0 19 8         2    0    2 1 20 9         2    1    0 0

## Getting The Bsod Error 0X000000F7? Fix It In 4 Simple Steps

Getting the BSoD error 0x000000f7? Fix it in 4 simple steps

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The BSoD error 0x000000f7 can be related to the Windows registry or corrupted system files.

To resolve this issue, make sure to update all your drivers manually or with a dedicated tool.

The stop code 0x000000f7 can also occur when you have faulty RAM, so, check if there are any problems with your computer memory.

A system restore is another viable solution that can help you solve this glitch easily.

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Launch it on your PC to find all the problematic drivers.

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Windows BSoD( Blue Screen of Deaths) issue 0x000000F7 can occur due to multiple reasons and often shows different error messages.

Some of the error 0x000000F7 messages include RIVER_OVERRAN_STACK_BUFFER, KMODE_EXCEPTION_NOT_HANDLED, or UNEXPECTED_KERNAL_MODE_TRAP.

The BSoD error with the stop code 0x000000f7 can be related to the chúng tôi which is an executable file associated with Windows Operating Systems.

This error can occur due to a bad RAM module, incompatible drivers, glitch in any of the recently installed Windows updates, or hardware issues as reported by the users in the Microsoft community forum.

In this article, we explore a few common solutions to fix the BSoD error 0x000000f7 in Windows computers.

How do I fix the BSoD error 0x000000f7?

Many BSoD errors are related to hardware issues or outdated drivers. Thus, make sure to have all your drivers up to date. You can do this manually from Device Manager.

It works with all versions of Windows and makes upgrading drivers a breeze. Outbyte Driver Updater may be set to find outdated drivers automatically.

Outbyte Driver Updater can assist you in automatically updating drivers and preventing PC harm caused by installing the incorrect driver version. It keeps up with the latest modifications, preventing the system from experiencing latency, system failures, and BSoD faults.

Expert tip:

2.  Run System File Checker

The SFC scan is a command-line tool that will scan your system for potential errors and resolve them on the way. So, it can also fix the BSoD with stop code 0x000000f7.

If you have any problems while running SFC, it stops or does not work at all on Windows 10, take a look at our dedicated guide in order to fix the issue.

3. Check for memory issues

One of the reasons for the error 0x000000f7 is a bad memory. If your system has a removable RAM module, try changing them.

Restart the device to see if the error is resolved. If you have a custom-built PC, you should be able to remove all the RAM modules. Remove all but one stick and boot the PC to see if the error is resolved.

Try these will all the RAM modules to see which memory kit is causing the error. In some cases, it could be the RAM slot that is causing the error, so avoid using the faulty RAM slot.

4. Use system restore point

The system restore process may take some time depending on the size of the restore point. The PC will restart once the restore process is complete and show a success message.

If you encounter any other BSoD errors and are curious why they happen, take a look at our guide including the most common causes for blue screens.

Still experiencing troubles? Fix them with this tool: