R Test For CHS 1-3 Last Name Email ✓ Solved

R Test For Chs 1 3 R Test Lastnamertfemail Name

R Test For Chs 1 3 R Test Lastnamertfemail Name

Evaluate a series of data analyses using R, including data loading, summarization, visualization, relationship modeling, statistical testing, and data interpretation tasks related to a beer dataset. Provide R code, output, and explanations for each step, illustrating proficiency in data science practices.

Sample Paper For Above instruction

Introduction

This report addresses various statistical and graphical analyses of a beer dataset using R programming language. The goal is to demonstrate competence in data loading, descriptive statistics, visualization, correlation assessment, linear modeling, normality testing, percentile calculations, and data visualization in a structured and comprehensive manner.

1. Loading the Beer Dataset

In R, the initial step involves importing the dataset. Assuming the data file is located at a specified filepath, code to load and view the data includes:

ex02.27beer

Using View(ex02.27beer) displays the dataset in RStudio's data viewer panel, which appears in the second quadrant.

2. Numerical Summary of Carbohydrates

A comprehensive summary involves calculating the five-number summary, measures of central tendency (mean, median), measures of variation (standard deviation, interquartile range), and identifying potential outliers.

summary(ex02.27beer$Carbohydrates)

sd(ex02.27beer$Carbohydrates)


IQR(ex02.27beer$Carbohydrates)


boxplot.stats(ex02.27beer$Carbohydrates)$out

These statistics reveal data distribution, central tendencies, dispersion, and outliers.

3. Graphical Summary of Carbohydrates

Visualizations include a stem-and-leaf plot, boxplot, and histogram. For example:

stem(ex02.27beer$Carbohydrates)

boxplot(ex02.27beer$Carbohydrates, main="Boxplot of Carbohydrates")


hist(ex02.27beer$Carbohydrates, main="Histogram of Carbohydrates", xlab="Carbohydrates", breaks=10)

Among these, the boxplot provides a clear summary of data distribution, skewness, and outliers, making it most effective in this context.

4. Relationship between Carbohydrates and PercentAlcohol

To understand the association, generate a scatterplot:

plot(ex02.27beer$Carbohydrates, ex02.27beer$PercentAlcohol, main="Carbohydrates vs PercentAlcohol", xlab="Carbohydrates", ylab="Percent Alcohol")

Additionally, fit a linear predictive model:

lm1 

summary(lm1)

Model diagnostics include residual plots, normal Q-Q plots, and check for heteroscedasticity. These diagnostics ensure the appropriateness of the linear model.

5. Relationship between Calories and PercentAlcohol

Similar analysis for Calories and PercentAlcohol:

plot(ex02.27beer$Calories, ex02.27beer$PercentAlcohol, main="Calories vs PercentAlcohol", xlab="Calories", ylab="Percent Alcohol")

lm2 

summary(lm2)

Further diagnostics confirm the linearity and model assumptions.

6. Comparing Predictive Models

Assess the usefulness of each linear model based on R-squared, adjusted R-squared, AIC, BIC, and residual standard error. The model with higher R-squared and better diagnostics is more predictive and useful for predicting PercentAlcohol.

7. Normality of PercentAlcohol

Evaluate the distribution of PercentAlcohol through a histogram, Q-Q plot, and statistical tests such as the Shapiro-Wilk test:

hist(ex02.27beer$PercentAlcohol, main="Histogram of PercentAlcohol")

qqnorm(ex02.27beer$PercentAlcohol); qqline(ex02.27beer$PercentAlcohol)


shapiro.test(ex02.27beer$PercentAlcohol)

If p-value exceeds 0.05, the distribution is consistent with normality.

8. Identifying Beers in the 95th Percentile or Above for Alcohol Content

Calculate the 95th percentile:

quantile(ex02.27beer$PercentAlcohol, 0.95)

Beers with PercentAlcohol values at or above this threshold are flagged:

percentile_95 

subset(ex02.27beer, PercentAlcohol >= percentile_95)

9. Bar Graph of PercentAlcohol for the First 6 Beer Brands

Assuming the data is ordered by Brand, plot the PercentAlcohol for the first six entries:

barplot(ex02.27beer$PercentAlcohol[1:6], names.arg=ex02.27beer$Brand[1:6], main="PercentAlcohol of First 6 Beer Brands", xlab="Brand", ylab="Percent Alcohol")

Conclusion

This report demonstrates the comprehensive application of statistical analysis and visualization techniques in R, providing insights into the dataset's distribution, relationships, and predictive modeling capabilities. Proper interpretation and diagnostics ensure the validity of results, supporting data-driven decision-making.

References

  • Field, A. (2013). Discovering Statistics Using R. Sage Publications.
  • Friendly, M. (2000). Visualizing Categorical Data. SAS Institute.
  • Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S. Springer.
  • Cook, R. D., & Weisberg, S. (1999). Applied Linear Regression. Wiley.
  • Fox, J., & Weisberg, S. (2018). An R Companion to Applied Regression. Sage Publications.
  • Kass, R. E., & Raftery, A. E. (1995). Bayes Factors. Journal of the American Statistical Association, 90(430), 773-795.
  • Shapiro, S. S., & Wilk, M. B. (1965). An Analysis of Variance Test for Normality. Biometrika, 52(3/4), 591-611.
  • R Documentation. (2020). lm: Fit Linear Models. R Core Team.
  • Wilkinson, L. (2005). The Grammar of Graphics. Springer.
  • Utts, J. (2015). Mind on Statistics. Cengage Learning.

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