Sample Report - Data Science Capstone

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Published

June 18, 2024

Introduction

What is “mehtod”?

This is an introduction to LASSO regression, which is a non-parametric estimator that estimates the conditional expectation of two variables which is random. The goal of a kernel regression is to discover the non-linear relationship between two random variables. To discover the non-linear relationship, kernel estimator or kernel smoothing is the main method to estimate the curve for non-parametric statistics. In kernel estimator, weight function is known as kernel function (Efromovich 2008). Cite this paper (Bro and Smilde 2014). The GEE (Wang 2014). The PCA (Daffertshofer et al. 2004)

This is my work and I want to add more work…

Methods

The common non-parametric regression model is \(Y_i = m(X_i) + \varepsilon_i\), where \(Y_i\) can be defined as the sum of the regression function value \(m(x)\) for \(X_i\). Here \(m(x)\) is unknown and \(\varepsilon_i\) some errors. With the help of this definition, we can create the estimation for local averaging i.e. \(m(x)\) can be estimated with the product of \(Y_i\) average and \(X_i\) is near to \(x\). In other words, this means that we are discovering the line through the data points with the help of surrounding data points. The estimation formula is printed below (R Core Team 2019):

\[ M_n(x) = \sum_{i=1}^{n} W_n (X_i) Y_i \tag{1} \] \(W_n(x)\) is the sum of weights that belongs to all real numbers. Weights are positive numbers and small if \(X_i\) is far from \(x\).

Another equation:

\[ y_i = \beta_0 + \beta_1 X_1 +\varepsilon_i \]

Analysis and Results

Data and Visualization

A study was conducted to determine how…

Code 
# loading packages 
library(tidyverse)
library(knitr)
library(ggthemes)
library(ggrepel)
library(dslabs)
Code 
# Load Data
kable(head(murders))
state abb region population total
Alabama AL South 4779736 135
Alaska AK West 710231 19
Arizona AZ West 6392017 232
Arkansas AR South 2915918 93
California CA West 37253956 1257
Colorado CO West 5029196 65
Code 
ggplot1 = murders %>% ggplot(mapping = aes(x=population/10^6, y=total)) 

  ggplot1 + geom_point(aes(col=region), size = 4) +
  geom_text_repel(aes(label=abb)) +
  scale_x_log10() +
  scale_y_log10() +
  geom_smooth(formula = "y~x", method=lm,se = F)+
  xlab("Populations in millions (log10 scale)") + 
  ylab("Total number of murders (log10 scale)") +
  ggtitle("US Gun Murders in 2010") +
  scale_color_discrete(name = "Region")+
      theme_bw()

Statistical Modeling

Conclusion

References

Bro, Rasmus, and Age K Smilde. 2014. “Principal Component Analysis.” Analytical Methods 6 (9): 2812–31.
Daffertshofer, Andreas, Claudine JC Lamoth, Onno G Meijer, and Peter J Beek. 2004. “PCA in Studying Coordination and Variability: A Tutorial.” Clinical Biomechanics 19 (4): 415–28.
Efromovich, S. 2008. Nonparametric Curve Estimation: Methods, Theory, and Applications. Springer Series in Statistics. Springer New York. https://books.google.com/books?id=mdoLBwAAQBAJ.
R Core Team. 2019. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org.
Wang, Ming. 2014. “Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments.” Advances in Statistics 2014.