Showing posts with label univariate linear regression in data science. Show all posts
Showing posts with label univariate linear regression in data science. Show all posts

Friday, March 13, 2020

Univariate linear regression in data science

>How to apply univariate linear regression in data science with R.

We are going to predict quantitative response Y, is one predictor variable, x where why has a dinner relationship with x.
Y=b0+b1+e
b0=intercept
b1=slope
e=error term.
The least squares choose the model parameters that minimise the sum of square (RSS) of predict the value of x values versus the actual Y values.

 data(anscombe)
>
> attach(anscombe)
>
> anscombe
   x1 x2 x3 x4    y1   y2    y3    y4
1  10 10 10  8  8.04 9.14  7.46  6.58
2   8  8  8  8  6.95 8.14  6.77  5.76
3  13 13 13  8  7.58 8.74 12.74  7.71
4   9  9  9  8  8.81 8.77  7.11  8.84
5  11 11 11  8  8.33 9.26  7.81  8.47
6  14 14 14  8  9.96 8.10  8.84  7.04
7   6  6  6  8  7.24 6.13  6.08  5.25
8   4  4  4 19  4.26 3.10  5.39 12.50
9  12 12 12  8 10.84 9.13  8.15  5.56
10  7  7  7  8  4.82 7.26  6.42  7.91
11  5  5  5  8  5.68 4.74  5.73  6.89
> #correlation of x1 and y1
> cor(x1, y1)
[1] 0.8164205
> cor(x2,y2)
[1] 0.8162365
> cor(x3,y3)
[1] 0.8162867
> cor(x4,y4)
[1] 0.8165214
> cor(x2, y1)
[1] 0.8164205
> #create a 2x2 grid for plotting
>
univariate linear regression in data science
FIG1

> par(mfrow=c(2,2))
> plot(x1, y1, main="Plot 1")
>
> plot(x2, y2, main="Plot 2")
>
> plot(x3, y3, main="Plot 3")
>
> plot(x4, y4, main="Plot 4")
> #Plot 1 appears to have a true linear relationship, Plot 2 is curvilinear, Plot
> 3 has a dangerous outlier, and Plot 4 is driven by the one outlier

Black-Scholes formula-R

 Black-Scholes formula-R > BlackScholes <- function(TypeFlag = c("c", "p"), S, X, Time, r, b, sigma) { TypeFla...