When modeling real world data for regression analysis, we observe that it is rarely the case that the equation of the model is a linear equation giving a linear graph. Most of the time, the equation of the model of real world data involves mathematical functions of higher degree like an exponent of 3 or a sin function. In such a scenario, the plot of the model gives a curve rather than a line. The goal of both linear and non-linear regression is to adjust the values of the model’s parameters to find the line or curve that comes closest to your data. On finding these values we will be able to estimate the response variable with good accuracy. In Least Square regression, we establish a regression model in which the sum of the squares of the vertical distances of different points from the regression curve is minimized. We generally start with a defined model and assume some values for the coefficients. We then apply the nls() function of R to get the more accurate values along with the confidence intervals. Syntax The basic syntax for creating a nonlinear least square test in R is − Following is the description of the parameters used − Example We will consider a nonlinear model with assumption of initial values of its coefficients. Next we will see what is the confidence intervals of these assumed values so that we can judge how well these values fir into the model. So let’s consider the below equation for this purpose − Let’s assume the initial coefficients to be 1 and 3 and fit these values into nls() function. When we execute the above code, it produces the following result − We can conclude that the value of b1 is more close to 1 while the value of b2 is more close to 2 and not 3.

Time series is a series of data points in which each data point is associated with a timestamp. A simple example is the price of a stock in the stock market at different points of time on a given day. Another example is the amount of rainfall in a region at different months of the year. R language uses many functions to create, manipulate and plot the time series data. The data for the time series is stored in an R object called time-series object. It is also a R data object like a vector or data frame. The time series object is created by using the ts() function. Syntax The basic syntax for ts() function in time series analysis is − Following is the description of the parameters used − Except the parameter “data” all other parameters are optional. Example Consider the annual rainfall details at a place starting from January 2012. We create an R time series object for a period of 12 months and plot it. Live Demo When we execute the above code, it produces the following result and chart − Jan Feb Mar Apr May Jun Jul Aug Sep 2012 799.0 1174.8 865.1 1334.6 635.4 918.5 685.5 998.6 784.2 Oct Nov Dec 2012 985.0 882.8 1071.0 The Time series chart − Different Time Intervals The value of the frequency parameter in the ts() function decides the time intervals at which the data points are measured. A value of 12 indicates that the time series is for 12 months. Other values and its meaning is as below − Multiple Time Series We can plot multiple time series in one chart by combining both the series into a matrix. When we execute the above code, it produces the following result and chart − The Multiple Time series chart −