This assignment involves 3 Case Problems. You are to use RStudio to complete this assignment. Case Problem 1: Heavenly Chocolates manufactures and sells quality chocolate products at its plant and retail store located in Saratoga Springs, New York. Two years ago, the company developed a web site and began selling its products over the Internet. Web site sales have exceeded the companys expectations, and management is now considering strategies to increase sales even further. To learn more about the web site customers, a sample of 50 Heavenly Chocolates transactions was selected from the previous months sales. Data showing the day of the week each transaction was made, the type of browser the customer used, the time spent on the web site, the number of web pages viewed, and the amount spent by each of the 50 customers are contained in the file Heavenly Chocolates. A portion of the data is shown in the table that follows: Table 1: Portion of the Data for Case Problem 1 Customer Day Browser Time (min) Pages Viewed Amount Spent ($) 1 Mon Chrome 12.0 4 54.52 2 Wed Other 19.5 6 94.90 3 Mon Chrome 8.5 4 26.68 4 Tue Firefox 11.4 2 44.73 5 Wed Chrome 11.3 4 66.27 6 Sat Firefox 10.5 6 67.80 7 Sun Chrome 11.4 2 36.04 8 Fri Firefox 10.5 6 67.80 9 Wed Firefox 12.7 3 70.94 10 Tue Chrome 24.7 7 68.73 Heavenly Chocolates would like to use the sample data to determine whether online shoppers who spend more time and view more pages also spend more money during their visit to the web site. The company would also like to investigate the effect that the day of the week and the type of browser have on sales. Managerial Report Use the methods of descriptive statistics to learn about the customers who visit the Heavenly Chocolates web site. Include the following in your report. Graphical and numerical summaries for the length of time the shopper spends on the web site the number of pages viewed, and the mean amount spent per transaction. Discuss what you learn about Heavenly Chocolates online shoppers from these numerical summaries. Summarize the frequency, the total dollars spent, and the mean amount spent per transaction for each day of week. Discuss the observations you can make about Heavenly Chocolates business based on the day of the week? Summarize the frequency, the total dollars spent, and the mean amount spent per transaction for each type of browser. Discuss the observations you can make about Heavenly Chocolates business based on the type of browser? Develop a scatter chart and compute the sample correlation coefficient to explore the relationship between the time spent on the web site and the dollar amount spent. Use the horizontal axis for the time spent on the web site. Discuss your findings. Develop a scatter chart and compute the sample correlation coefficient to explore the relationship between the number of web pages viewed and the amount spent. Use the horizontal axis for the number of web pages viewed. Discuss your findings. Develop a scatter chart and compute the sample correlation coefficient to explore the relationship between the time spent on the web site and the number of pages viewed. Use the horizontal axis to represent the number of pages viewed. Discuss your findings. Question 1 Answer Format: Table 2: Question 1 Answer Format Summary Statistic Time (min) Pages Viewed Amount Spent ($) Mean Median Standard Deviation Range Min Max Sum Provide R code Cut and paste graphs. Case Problem 2: Hamilton County Judges Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed, some of the cases are reversed. Kristen DelGuzzi of the Cincinnati Enquirer newspaper conducted a study of cases handled by Hamilton County judges over a three-year period. Shown in the table below are the results for 182,908 cases handled (disposed) by 38 judges in Common Pleas Court, Domestic Relations Court, and Municipal Court. Two of the judges (Dinkelacker and Hogan) did not serve in the same court for the entire three-year period. The purpose of the newspapers study was to evaluate the performance of the judges. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which judges were doing a good job and which were making too many mistakes. You are called in to assist in the data analysis. Use your knowledge of probability and conditional probability to help with the ranking of the judges. You also may be able to analyze the likelihood of appeal and reversal for cases handled by different courts. Common Please Court: Table 3: Data for Problem Case 2 Judge Total Cases Disposed Appealed Cases Reversed Cases Cartolano 3037 137 12 Crush 3372 119 10 Dinkelacker 1258 44 8 Hogan 1954 60 7 Kraft 3138 127 7 Mathews 2264 91 18 Morrissey 3032 121 22 Nadel 2959 131 20 Ney Jr. 3219 125 14 Niehaus 3353 137 16 Nurre 3000 121 6 O'Connor 2969 129 12 Ruehlman 3205 145 18 Sundermann 955 60 10 Tracey 3141 127 13 Winkler 3089 88 6 TOTAL 43945 1762 199 Managerial Report: The probability of cases being appealed and reversed. The probability of a case being appealed for each judge. The probability of a case being reversed for each judge. Case Problem 3: Complete Linkage Clustering of Utility Companies To inform political leaders and economists discussing the deregulation of electric and gas utilities, data on eight numerical variables from utility companies have been grouped using hierarchical clustering based on Euclidean distance to measure dissimilarity between observations and complete linkage as the agglomeration method. Questions: Based on the following dendrogram, what is the most appropriate number of clusters to organize these utility companies? A dendogram showing distance on the y axis and cluster on the x axis. There are 21 individual observations. The first stage of clustering resultis in 11 clusters. The second stage results in 9 clusters. The third results in 4 clusters. The fourth results in 2 clusters, the fifth is the final single cluster. The between-cluster distance is 2.577. Using the following data on the Observations 10, 13, 4, and 20, confirm that the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units as displayed in the dendrogram. Case Problem 3 Table Observation 10 Observation 13 Observation 4 Observation 20 d104 d1020 d134 d1320 Income/Debt 0.032 0.195 -0.2051 0.466 Return 0.741 0.875 0.207 0.474 Cost 0.7 0.748 -0.04 -0.49 Load -0.892 -0.735 -0.219 0.655 Peak -0.173 1.013 -0.943 0.083 Sales -0.693 -0.489 -0.702 -0.458 % Nuclear 1.62 2.275 1.328 1.733 Total Fuel Costs -0.863 -1.035 -0.724 -0.721