Data 301 Lab 6

Data 301 Lab 6httpspeopleokubccarlawrencteaching301labs301

This lab involves using R for data analysis, including data loading, cleaning, summarizing, visualization, and conducting hypothesis tests. Students can work alone or in pairs, with submission from one member only, including both names in the files if working in pairs.

Objectives include mastering data manipulation and visualization techniques in R, performing one-sample and two-sample t-tests on datasets, and interpreting the results.

Paper For Above instruction

Introduction

This paper discusses the analytical tasks involved in Lab 6 of Data Analytics course, focusing on data handling, visualization, and hypothesis testing using R. The dataset encompasses sensor data in CSV format and sales data in CSV format; the goal is to derive insights through appropriate data processing and inferential statistical testing.

Reading and Summarizing Sensor Data

The initial step involves importing sensor data from a CSV file named 'sensor.csv'. Using R's read.csv() function, the dataset is loaded, and the first 20 rows are displayed via head() to get an initial understanding of its structure. The dataset contains multiple observations, including sensor readings from different sites and sensors. To clean the data, a subset called sensors_clean is created, which includes only observations where sensor values are between 0 and 100, inclusive. This ensures that analyses are based on plausible sensor readings, eliminating potential outliers or erroneous data points.

Data summarization involves creating a list called data_summary, which offers key insights: the count of valid readings, the minimum, mean, and maximum sensor values; range; maximum reading specifically from sensor 2 at site 2; and total number of observations from site 1 sensor 2. These summaries provide a broad overview of data distribution, sensor performance, and site-specific readings. Functions like length(), min(), mean(), max(), and range() are instrumental in generating these metrics.

Data visualization follows, with a histogram illustrating the distribution of all sensor values, helping identify potential skewness or outliers. Additionally, a boxplot comparing the three different sensors visually reveals differences in their distributions. To produce the boxplot, sensorid is converted to a factor with as.factor(), ensuring proper grouping. Visualization tools like hist() and boxplot() are used, or alternatively ggplot2 functions for more advanced plotting, as per the course notes.

Hypothesis Testing: Overall Mean of Sensor Values

The second analytical task involves testing whether the mean value of all sensor readings is less than 45. The null hypothesis (H0) states that the mean sensor value is greater than or equal to 45, whereas the alternative hypothesis (H1) posits that the mean is less than 45. An appropriate one-sample t-test, such as t.test() in R, is conducted on the sensor data.

Based on the test output, a determination is made whether to reject H0. If the p-value is below the significance threshold (typically 0.05), H0 is rejected, indicating sufficient evidence to conclude that the mean sensor value is statistically less than 45. Conversely, a failure to reject H0 suggests insufficient evidence, and the conclusion is that the mean is not significantly less than 45.

Comparing Sensor Values Across Sites

The third analysis aims to compare sensor readings between site 1 and site 2. A new dataframe called new_data is created, filtering observations from these two sites only. The hypotheses are: H0 posits no difference in mean sensor values between site 1 and site 2; H1 suggests there is a difference.

A two-sample t-test is performed to compare the means between these sites. The decision to reject or fail to reject the null hypothesis depends on the p-value obtained. Rejection indicates that the sites differ significantly in sensor readings, implying possible environmental or operational differences affecting sensor measurements.

Sales Data Analysis and Regression Modeling

The final task involves analyzing an advertising dataset, 'advertising.csv', which contains sales figures and advertising budgets for TV, Radio, and Newspaper. The dataset is loaded into a dataframe named advertising, with the last 15 rows displayed via tail() for review of recent data points. The goal is to investigate how advertising budgets influence sales.

Relationships between sales and each advertising medium are visualized through scatterplots created with plot(), for instance, plot(Radio, Sales). These plots reveal potential correlations and inform regression modeling.

Subsequently, a linear regression model is developed to predict sales based on TV advertising spend using lm(). The model's summary provides coefficients, R-squared, and significance levels, demonstrating the strength of the relationship. The regression line is plotted onto a scatterplot of sales and TV budget, with the line rendered in red for visual clarity.

Conclusion

This comprehensive analysis showcases essential data science skills—data cleaning, visualization, hypothesis testing, and regression modeling—in R. These techniques enable data analysts to extract meaningful insights, verify assumptions, and predict outcomes, fundamental to effective data-driven decision-making.

References

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  • Fox, J., & Weisberg, S. (2018). An R Companion to Applied Regression. Sage Publications.
  • Chang, W. (2021). ggplot2: Create Elegant Data Visualisations Using the Grammar of Graphics. Springer.
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  • Kutner, M. H., et al. (2005). Applied Linear Statistical Models. McGraw-Hill Education.
  • Friedman, J., et al. (2001). The Elements of Statistical Learning. Springer.

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