Linear Regression Online Courses

A simple method to plot a graph of X and Y is to use the Google Sheets linear regression. In Google Sheets, the linear regression line plots the data with the help of a scatter plot. You need to choose the data range to plot (including headers). Next, open the Insert menu, and choose the Chart option A. It will insert a new chart. The Chart Editor sidebar will be shown.

The linear regression equation depicts the linear relationship between X and Y variables. It is identical to the slope formula.

Linear Regression Formula:

Y= nX + m
The least-squares is the greatest technique to fit a regression line in an XY plot. It determines the best-fitting line for a specific data set. This is because it decreases the sum of squares of the vertical variance from every data point to the line.
If a point accurately rests on the fitted line, the value of its upright variance is 0. The reason is the variations are first squared and added. Hence, their negative and positive values will not be annulled. The corresponding straight line is the least-squares regression line (LSRL).
Let’s assume X as an independent variable and Y as a dependent variable. The equation of the population regression line:
Y = α0 + α1X

here, α0: constant

α1: regression coefficient

If a random sample of observations is considered, the equation of the regression line is:
ŷ = α0+ α1x

here x: independent variable

ŷ: the predicted value of the dependent variable

α0: constant

α1: regression coefficient

A linear regression line equation is:
Y = m + nX

Here the X (independent) variable is plotted on the X-axis and the Y (dependent) variable on the Y-axis. The m is the intercept (value of y when x = 0), and n is the slope of the line.

Multiple Regression Line Formula:

y= m +n1x1 +n2x2 + n3x3 +…+ ntxt + u

Examples to solve the linear regression equation:

Let’s find a linear regression equation for the two sets of data:

x1 = 2, x2 = 4, x3 = 6, x4 = 8

y1 = 3, y2 = 5, y3 = 7, y4 = 9

Find the value of Σx, Σy, Σx2, and Σxy.

Based on the given data set,

x12 = 4, x22 = 16, x32 = 36, x42 = 64

x1y1 = 6, x2y2 = 20, x3y3 = 42, x4y4 = 72

Σx = x1+ x2 + x3 + x4 = 20

Σy = y1+ y2 + y3 + y4 = 24

Σx2 = x12+ x22 + x32 + x42 = 120

Σxy = x1y1 + x2y2 + x3y3 + x4y4 = 140

Using the formula of the linear equation y=m+nx, calculate the values of m and n.

Using the formula, find the value of a and b

here s = number of datasets = 4

Now put all the calculated values in the above equations of m and n.

m = ((24×120) − (20×140))/((4×120)−400)

m = 1

n = 4((140) – (20×24))/((4×120)−(400))

n = -17

Hence, m = 1 and n = -17
So, the linear equation Y = m + nx is now Y = 1 - 17x

When you pursue one of the best linear regression courses, you become familiar with all aspects of linear regression, including how to find the equation of the regression line. The corresponding linear regression training aims to acquaint students with how to plot the regression line from the derived equation.

The standard form of the linear regression line equation is y = mx + c. It denotes an equation of a line with a y-intercept of c and a gradient of m. It needs the y-intercept ‘c’ of the line and the slope value ‘m’. Another name for this equation is the slope-intercept form. In machine learning and artificial intelligence, this equation helps predict the values depending on the values of the input variable.

Here is the description of the slope and intercept:

Slope: The alphabet m denotes the gradient or slope of the line. Its value can be positive, negative, or zero. Furthermore, one can calculate from the tangent of the inclination angle of this line concerning the X-axis or a line parallel to the X-axis.

Intercept: The alphabet c denotes the intercept of the line. This intercept measures the length at which the line crosses the y-axis from the origin. The intercept is also indicated through the point (0, c) on the Y-axis. At this point, the line is passing. The point (0, c) is c units far from the origin.

How to derive y = mx + c equation:

You can derive this equation from other significant forms of equations of a line. A few of these forms of equations are as below:

Deriving the Slope Formula:

The slope formula helps to derive the y = mx + c equation. It takes (0, c) point on the Y-axis and an arbitrary point (x, y) over the line. Using these two points, find the slope ‘m’. It first calculates the variance of the y coordinates of these two points and then divides it by the difference of the x coordinates among them.

m = (y - c)/(x - 0)

m = (y - c)/(x)

mx = y - c

So, y = mx + c

Hence, the Slope Formula helps derive the line equation's slope-intercept form.

Point Slope Form:

To derive this form of the line equation, you need the slope of the line and a point. Suppose the slope of the line is m, and the point is (0,c). These two values help find the point-slope form equation as below:

(y - c) = m(x - 0)

y - c = mx

So, y = mx + c

Hence, the Point-Slope form helps derive the line's y = mx + c equation.

To calculate the correlation coefficient, firstly, you need to determine the variables' covariance. The covariance value is then divided by the multiplication of standard deviations of the given variables

Here is the equation to find the correlation coefficient:

ρxy = Cov(x,y) /σxσy

here, ρxy: Pearson's product-moment correlation coefficient

Cov(x,y): Covariance of variables x and y

σx: Standard deviation of x

σy: Standard deviation of y

In the above formula, the term Cov(x,y) is covariance. It provides the joint relationship among two random variables. Its formula is:

here,

n = Total number of values of x or y

x,y = random variables

xi = data value of x

yi = data value of y

x’= mean of all the values of x

y’= mean of all the values of y

The formula for the correlation coefficient is:

Here,

n = Total number of values of x or y

Σx = Total of all values of the first variable

Σy = Total of all values of the second variable

Σxy = Sum of products of x and y values

Σx2 = Sum of squares of the first variable

If one independent variable is considered, it is known as simple linear regression. It is known as multiple linear regression if numerous independent variables are used. Simple linear regression helps you estimate the relationship between two quantitative variables. You can use the simple linear regression Google Sheets to analyse simple regression further accurately.

Simple linear regression is practical when you want to know:The value of a dependent variable at a specific value of the independent variable (for example, the number of sales at a specific festive season)

How powerful the relationship between two variables is (for example, the relationship between the number of sales and the festive season)

Assumption of Simple Linear regression:
It assumes a linear relationship between the independent and dependent variables. The best fit line across the data points is a straight line.

Objectives of Simple Linear regression algorithm:

The examples include the relationship between salary and experience, investment and sales, income and expenditure, etc., to model the relationship between the two variables. Forecasting observations like weather forecasting based on temperature, a company's income based on the investment in a year, etc.

The equation of the Simple Linear Regression model:

y= α0+ α1x+ ε

here,

α0= the intercept of the regression line (obtained with x = 0)

α1= the slope of the regression line (denotes whether the line is increasing or decreasing)

ε = the error term.

Let’s understand Simple Linear Regression with a practical example
For example, a social researcher wants to establish the relationship between salary and happiness. Suppose there are 200 people surveyed whose salary ranges from 20k to 70k, and they are asked to rank their happiness on a scale of 1 to 5.

In the above example, the independent variable is salary, the dependent variable is happiness, and both are quantitative. Hence, you can perform a regression analysis to check if there is a linear relationship between them.

i. Easy to interpret:

Linear Regression is easy to implement and easy to interpret the output coefficients. Its models can be trained efficiently and easily, even on those systems with comparatively low computational power compared to the other complex algorithms. Pursuing linear regression training or one of the best linear regression courses helps you learn all the crucial aspects of linear regression. Moreover, the linear regression online course offers excellent convenience and flexibility.

ii. Less complexity:

When you detect the linear relationship between the dependent and independent variable, the linear regression algorithm is more suitable than other machine learning algorithms due to its ease. Moreover, the equations of linear regression are easy to interpret and easy to master.

Linear regression perfectly fits linearly separable datasets and is frequently used to determine the nature of the relationship among variables. Obtaining a linear regression certification implies comprehending the less complex linear regression models.

iii. Reduced over-fitting:

Although linear regression is prone to over-fitting, one can prevent it with the help of certain dimensionality, reduction techniques, cross-validation, and regularisation (L1 and L2) techniques. The regularisation technique is easy to implement and can competently reduce the complexity of a linear regression function. Hence, it decreases the risk of overfitting.

i. Assumes independence between variables:

The linear regression algorithm assumes a linear relationship between dependent and independent variables. It assumes a straight-line relationship and predicts the independence between attributes.

ii. Incomplete description of relationships among variables:

Linear regression focuses on the relationship between the mean of the independent variables and the dependent variables. The mean is not a comprehensive description of a single variable. Hence, linear regression is not a complete description of relationships between variables.

iii. Susceptible to underfitting:

Underfitting occurs when a machine learning model cannot capture the data. Typically, this situation is observed when the hypothesis function can’t correctly fit the data. Linear regression undertakes a linear relationship between input and output variables. Hence, it can’t correctly fit the complex data

iv. Low accuracy:

In most real-life scenarios, there doesn’t exist a linear relationship among the dataset's variables. Therefore, a straight line doesn't correctly fit the data. For such cases, a more complex function can effectively capture the data leading linear regression models to show low accuracy.

A dataset’s outliers are variances or extreme values that diverge from the other data points of a particular distribution. These data outliers can significantly degrade the performance of a machine learning model. Hence, they usually lead to low accuracy of the models.

Practical Application-1:

Businesses frequently use linear regression to determine the relationship between income and advertising expenditure. We can understand this application from the perspective of linear regression.

For example, businesses may use a simple linear regression model where advertising expenditure is considered the predictor variable and income is the response variable.

So, the equation of the regression model becomes:

Income = β0 + β1 (ad expenditure)

Coefficient β0 shows the total expected income when ad expenditure is zero.

Coefficient β1 shows the average change in the total income when ad expenditure increases by one unit (for example, one dollar).

If the β1 value is negative, there is more ad expenditure and less income.

If the β1 value is close to zero, the ad expenditure has little impact on income.

If β1 is positive, more ad expenditure is linked with more income.

Based on the value of β1, an organisation can decide whether to increase or decrease its ad spending.

Practical Application-2:

Medical researchers frequently use the linear regression algorithm to determine the relationship between patients' blood pressure and drug dosage.

Suppose the researchers observe different drug dosages in patients and notice the change in their blood pressure. This application can be mapped as a simple linear regression model, with dosage as the predictor variable and blood pressure as the response variable.

So, the equation of the linear regression model will be:

Blood pressure = β0 + β1 (drug dosage)

Coefficient β0 shows the expected blood pressure when drug dosage is zero.

Coefficient β1 shows the average change in patients' blood pressures when drug dosage increases by one unit.

If the β1 value is negative, the drug dosage increases with a decrease in blood pressure.

If the β1 value is close to zero, the drug dosage increases without changing blood pressure.

If β1 is positive, the drug dosage increases with an increase in blood pressure.

Based on the value of β1, medical researchers may alter the drug dosage for the patient.

Practical Application-3:

Data scientists for professional dance teams usually use the linear regression model to determine the effect of various dance training programs on dancers’ performance.

For example, suppose data scientists want to examine how weekly cardio sessions and Zumba sessions influence the total points a dancer scores. In this case, make a multiple linear regression model with the help of cardio sessions and Zumba sessions as the predictor variables and total score points as the response variable.

The equation of the linear regression model will be:

Total points scored = β0 + β1 (cardio sessions) + β2 (zumba sessions)

Coefficient β0 shows the predictable points a dancer scores who don’t participate in cardio and Zumba sessions.

Coefficient β1 shows the average change in total points scored when weekly cardio sessions increase by one. Here, the assumption is the number of weekly Zumba sessions stays unchanged.

Coefficient β2 shows the average change in total points scored when weekly Zumba sessions increase by one. Here, the assumption is the number of weekly cardio sessions stays unchanged.

Based on the β1 and β2 values, the data scientists recommend each dancer in which session they must participate to maximise their points.

The following section highlights major advantages of pursuing an online Tableau course over an offline one:

Training from industry experts:
The superlative aspect of pursuing a linear regression online course is that candidates will not suffer political limitations when learning. You can apply for any available Tableau online courses depending on your previous knowledge of this domain, budget, and schedule.

Plenty of offline Tableau courses may not have qualified and experienced industry experts or may include only a few industry experts. Conversely, any linear regression online course is fully equipped with sufficient numbers of trained and experienced industry experts. Therefore, the students attain enough guidance and can solve their doubts in a user-friendly manner.

In any Tableau course, the instructors hold the practical experience and accurately know how to teach each Tableau and linear regression concept. However, offline mentors might lack this aspect.

Training from industry experts:

Leading online Tableau and linear regression courses derive inspiration for projects from practical scenarios. It assists the learners in perceiving the existing market condition and understanding patterns existing in the data visualisation. Moreover, it opens exciting opportunities to learners hoping to get into reputable organisations.

Additional benefits of online Tableau courses compared to offline Tableau courses:

• Good choice for freshers, students, job seekers, and professionals
• Imparts Tableau teaching with Live projects and Demo projects
• Thorough guidance is provided with the backup classes and video-recorded classes
• Provides remote assistance for all-inclusive support to students
• Each online batch has a limited number of students

• Overview and uses of Tableau
• Tableau Basic Reports
• Custom SQL
• Tableau charts
• Tableau Advanced Reports
• Tableau dashboards
• Tableau calculations & filters
• Tableau data server
• Tableau server UI

The factors influencing the Tableau industry growth in the period 2024-25 are increasing execution of cloud computing services, increasing demand for data generation, high demand for Internet penetration, enhanced infrastructural development, and the upward trend of Bring-Your-Own-Device (BYOD).

The Tableau industry’s market value in the period 2024-25 is$1,016.5 Mn

This industry provides the services likely to accelerate with the continual developments in business intelligence technologies.

Tableau is the simplest visualisation tool for data handling. Certainly, automation requires a huge volume of data analyses, and Tableau serves crucial data for that. Furthermore, Tableau is also producing its personal space in domains, for example, business intelligence and data analytics. From this aspect, we can understand the importance of linear regression in data analytics.

Nowadays, many organisations are gradually moving towards the adaptation of Tableau. Ultimately, this leads to the creation of myriad Tableau career opportunities in India. Before the year 2022 completes, there will be an enormous demand for data scientists and data professionals well versed in Tableau.

In India, the demand for the Tableau course is very high since it derives essential information from the available data for which skilled data professionals are needed. On the other hand, an incompetent data professional can’t deal with the tasks of data analyses and data science in Tableau.

Candidates completing the Tableau course can effectively deal with the assigned duties in any job role like data analysts, data professionals, business analysts, and more. It requires professional intelligence to deal with sensitive data. As a result, it creates a huge demand for skilled and certified Tableau professionals. Furthermore, the massive demand for linear regression models in machine learning applications increases the need for pursuing Tableau courses in India.

If you have made up your mind to work in an MNC, the likelihood of getting recruited in any of the below job profiles can be increased after you finish the Tableau course in India:

• Consultant in Tableau
• Data Analyst
• Business Analyst

Here is the list of companies providing Tableau career opportunities in India:

• Dell
• Facebook
• Sony Electronics
• Hinduja Global Solutions
• Capgemini Technology Services
• Brickwork India Private Limited
• Pathfinder Management Consulting India Limited
• General Motors
• Verizon
• Applied Systems

In India, the average salary offered to Tableau Specialists is approx. INR 14 lac per year. Experienced Tableau Specialists can receive a salary up to 20 lac per year.

The salary of a Tableau Specialist can differ based on several factors. Here we outline a few factors:

• Salary based on employer
• Salary based on the job location
• Salary based on job titles

i. Salary based on the employer:

Source

ii. Salary based on job location:

In the USA, the salaries for Tableau specialists barely vary according to location. But in India, the economy of cities prominently influences the average salary offered to them. For example, in Delhi, a Tableau specialist with over 8 years of experience can earn up to INR 15 LPA.

iii. Salary based on Job titles:

In India, the starting salary of a Tableau specialist is approx. INR 8.5 lac per year.

The average salary of Tableau Specialists abroad is $65,000/year. For highly experienced and skilled Tableau Specialists, the salary is up to $132,000 annually in the U.S.

A Tableau Specialist's salary abroad can vary based on many factors. Here we outline a few factors:

• Salary based on the employer
• Salary based on job titles
• Salary based on skills

1. Salary based on the employer:

Source

2. Salary based on job titles:

Source

iii. Salary based on skills:

Over and above the general knowledge of computer applications, candidates equipped with other pertinent skills can obtain higher-paying jobs in different countries. Some of these skills are the cutting-edge business intelligence technologies such as Microsoft Power BI and Oracle BI.

The knowledge and working experience with SQL Server Data Tools, namely SQL Server Integration Services (SSIS), SQL Server Analytics Services (SSAS), and SQL Server Reporting Services (SSRS), can assure admirable paying jobs for the Tableau Specialists abroad.

The know-how of ETL Tools (including Talend and Informatica) can enhance your chances of grabbing an exceptional job as a Tableau Specialist Abroad.