DataScienceUsingR-Dr.P.Rajesh.PRESENTATION
- 1. Data Science using R P. Rajesh, Assistant Professor, PG Department of Computer Science C.Mutlur, Chidambaram
- 2. Linear Regression Regression analysis is a very widely used statistical tool to establish a relationship model between two variables. One of these variable is called predictor variable whose value is gathered through experiments. The other variable is called response variable whose value is derived from the predictor variable. Mathematically a linear relationship represents a straight line when plotted as a graph. A non-linear relationship where the exponent of any variable is not equal to 1 creates a curve. The general mathematical equation for a linear regression is − y = ax + b Following is the description of the parameters used − y is the response variable. x is the predictor variable. a and b are constants which are called the coefficients.
- 3. How much money should you allocate for gas? You approach this problem with a science-oriented mindset, thinking that there must be a way to estimate the amount of money needed, based on the distance you're travelling. At this point these are just numbers. It's not very easy to get any valuable information from this spreadsheet. "If I drive for 1200 miles, how much will I pay for gas?"
- 4. 2 2 i i i i i i x x n y x y x n a i i x a y n b 1 y = ax + b Sl.No. Total Miles (x) Total Payed (y) x*x x*y 1 390 36.66 152100 14297.4 2 403 37.05 162409 14931.15 3 396.5 34.71 157212.25 13762.52 4 383.5 32.5 147072.25 12463.75 5 321.1 32.63 103105.21 10477.49 6 391.3 34.45 153115.69 13480.29 7 386.1 36.79 149073.21 14204.62 8 371.8 37.44 138235.24 13920.19 9 404.3 38.09 163458.49 15399.79 10 392.6 38.09 154134.76 14954.13 11 386.49 38.74 149374.5201 14972.62 12 395.2 39 156183.04 15412.8 13 385.5 40 148610.25 15420 14 372 36.21 138384 13470.12 15 397 34.05 157609 13517.85 16 407 41.79 165649 17008.53 17 372.33 30.25 138629.6289 11262.98 18 375.6 38.83 141075.36 14584.55 19 399 39.66 159201 15824.34 7330.32 696.94 2834631.899 269365.1
- 5. Visualize the Regression Graphically # Create the predictor and response variable. x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131) y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48) relation <- lm(y~x) # Give the chart file a name. png(file = "linearregression.png") # Plot the chart. plot(y,x,col = "blue",main = "Height & Weight Regression",abline(lm(x~y)),cex = 1.3,pch = 16,xlab = "Weight in Kg",ylab = "Height in cm") # Save the file. dev.off()
- 6. Steps to Establish a Regression A simple example of regression is predicting weight of a person when his height is known. To do this we need to have the relationship between height and weight of a person. The steps to create the relationship is Carry out the experiment of gathering a sample of observed values of height and corresponding weight. Create a relationship model using the lm() functions in R. Find the coefficients from the model created and create the mathematical equation using these Get a summary of the relationship model to know the average error in prediction. Also called residuals. To predict the weight of new persons, use the predict() function in R. Input Data Below is the sample data representing the observations − lm() Function This function creates the relationship model between the predictor and the response variable. Syntax The basic syntax for lm() function in linear regression is − lm(formula,data)
- 7. Create Relationship Model & get the Coefficients x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131) y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48) # Apply the lm() function. relation <- lm(y~x) print(relation) Output Call: lm(formula = y ~ x) Coefficients: (Intercept) x -38.4551 0.6746
- 8. predict() Function Syntax The basic syntax for predict() in linear regression is − predict(object, newdata) Following is the description of the parameters used − object is the formula which is already created using the lm() function. newdata is the vector containing the new value for predictor variable. Predict the weight of new persons # The predictor vector. x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131) # The response vector. y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48) # Apply the lm() function relation <- lm(y~x) # Find weight of a person with height 170. a <- data.frame(x = 170) result <- predict(relation,a) print(result) When we execute the above code, it produces the following result − 1 76.22869
- 9. In order to answer this question, you'll use the data you've been collecting so far, and use it to predict how much you are going to spend. The idea is that you can make estimated guesses about the future — your trip to Vegas — based on data from the past. You end up with a mathematical model that describes the relationship between miles driven and money spent to fill the tank. Once that model is defined, you can provide it with new information — how many miles you're driving from San Francisco to Las Vegas. The model will predict how much money you're going to need.
- 10. Multiple Regression Multiple regression is an extension of linear regression into relationship between more than two variables. In simple linear relation we have one predictor and one response variable. But in multiple regression we have more than one predictor variable and one response variable. The general mathematical equation for multiple regression is − y = a + b1x1 + b2x2 +...bnxn Following is the description of the parameters used − y is the response variable. a, b1, b2...bn are the coefficients. x1, x2, ...xn are the predictor variables. We create the regression model using the lm() function in R. The model determines the value of the coefficients using the input data. Next we can predict the value of the response variable for a given set of predictor variables using these coefficients.
- 11. lm() Function This function creates the relationship model between the predictor and the response variable. Syntax The basic syntax for lm() function in multiple regression is − lm(y ~ x1+x2+x3...,data) Following is the description of the parameters used − • formula is a symbol presenting the relation between the response variable and predictor variables. • data is the vector on which the formula will be applied.
- 13. R Script Multiple Regression # Capture the in R format Year <- c(2017,2017,2017,2017,2017,2017,2017,2017,2017,2017,2017,2017,2016,2016,2016, 2016,2016,2016,2016,2016,2016,2016,2016,2016) Month <- c(12, 11,10,9,8,7,6,5,4,3,2,1,12,11,10,9,8,7,6,5,4,3,2,1) Interest_Rate <- c(2.75,2.5,2.5,2.5,2.5,2.5,2.5,2.25,2.25,2.25,2,2,2,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75, 1.75,1.75,1.75) Unemployment_Rate <- c(5.3,5.3,5.3,5.3,5.4,5.6,5.5,5.5,5.5,5.6,5.7,5.9,6,5.9,5.8,6.1,6.2,6.1,6.1,6.1,5.9,6.2,6.2,6.1) Stock_Index_Price <- c(1464,1394,1357,1293,1256,1254,1234,1195,1159,1167,1130,1075,1047,965,943,958,97 1,949,884,866,876,822,704,719)
- 14. # Check the Linearity the corresponding data is correct or not plot(x=Interest_Rate, y=Stock_Index_Price)
- 16. # Capture the in R format student <- c(1,2,3,4,5,6,7,8,9,10) testscore <- c(100,95,92,90,85,80,78,75,72,65) IQ <- c(125,104,110,105,100,100,95,95,85,90) studyhrs <- c(30,40,25,20,20,20,15,10,0,5) # Check the Linearity the corresponding data is correct or not plot(x=testscore, y=IQ) plot(x=IQ, y=studyhrs) #================================================== # Predict Test Square using IQ and Study Hrs relation <- lm(testscore ~ IQ + studyhrs) a <- data.frame(IQ=120,studyhrs=40) result <- predict(relation,a) print(result) #================================================== # Predict IQ using Test Square and Study Hrs relation <- lm(IQ ~ testscore + studyhrs) a <- data.frame(testscore=50,studyhrs=25) result <- predict(relation,a) print(result) #================================================== # Predict IQ using Test Square and Study Hrs relation <- lm(studyhrs ~ IQ + testscore ) a <- data.frame(IQ=140, testscore=90) result <- predict(relation,a) print(result)