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COURSE PROJECT PART A 7 INTRODUCTION In statistics, exploratory data analysis is considered a data analysis method, which requires various techniques for analysis (what is exploratory data analysis?). It is usually the first step in a data analysis project. In this paper, I will use graphs and numerical techniques to summarize data to analyze a given set of variables. A sample of 100 business activities was conducted in the following five variables: 1. Sales-Represents the sales volume this week. 2. Calls-indicates the number of sales calls made this week. 3. Time-represents the average time of each call this week. 4. Year-represents the number of years working in the call center. 5. Type-represents the type of training employees receive. INDIVIDUAL INTERPRETATION OF VARIABLES The data discussed below has variables such as calls, time and years. Below is their interpretation and graphical representation. X1 (number of sales calls made this week) Numerical Analysis Mean 160.33 Median 160.5 Mode Standard Deviation 19.26 The above analysis illustrates measures of central tendency (mean, median, and mode) and measures of change (standard deviation). In this example, the average value indicates that the call center's average number of calls per week is 160.33 calls. The median (160.5 calls) is very close to the mean, indicating that this data set may act as a normal distribution (must be confirmed). The standard deviation of 19.26 indicates approximately 95%. Graphical Analysis Frequency Distribution Table Below is the frequency distribution table for X1. *Table missing here* Histogram ( Bar chart ) The bar chart shows the total of similar frequencies for all groups in the 125-205 group, while the frequencies in the 196-200 group and 201-205 group decreased significantly. Some data points are concentrated near the distribution center, but not as obvious as the "weekly sales" variable. A histogram is a chart that allows you to discover and display the basic frequency distribution (shape) of a set of continuous data. This allows checking the basic distribution of data (for example, normal distribution), outliers, skewness, etc. This histogram shows that the data is not normally distributed and has several discrete intervals. It shows the three highest points, and the graphical representation depicts most sales calls between 171-175 calls. Similarly, the average data has many ups and downs. This reflects the various cycles that the business may experience. Box Plot *The chart of Box-Whisker’s Plot missing here* X2 (average time per call this week) *Continue to work on X2 and X3 in the same way: numerical analysis and chart analysis* INTERPRETATION OF VARIABLE PAIRINGS There may be a positive or negative correlation between the two variables. This relationship can be understood through statistical correlation analysis. We can find the following correlation coefficient. Pairing One: Sales (Y) vs. Calls (X1) Figure 10. Scatter Plot of Sales (Y) vs Calls (X1) This variable has a positive correlation of 0,330919. According to the analysis, these variables are positively correlated. This means that as sales increase, so will the number of calls. For the number 0,330919, the relationship is moderately positive. The more calls you make, the more likely the call center agent is to ensure sales. *Continue to work on Pairing Two: Sales (Y) vs. Times (X2) and Pairing Three: Sales (Y) vs. Years (X3) * CONCLUSION REFERENCE Introduction Your instructor will provide you with a data file that includes data on five variables: SALES represents the number of sales made this week. CALLS represents the number of sales calls made this week. TIME represents the average time per call this week. YEARS represents years of experience in the call center. TYPE represents the type of training the employee received. Part A: Exploratory Data Analysis Preparation · Open the files for the course project and the data set. · For each of the five variables, process, organize, present and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use Excel as much as possible, explaining what the results reveal. Some of the following graphs may be helpful: stem-leaf diagram, frequency/relative frequency table, histogram, boxplot, dotplot, pie chart, bar graph. Caution: not all of these are appropriate for each of these variables, nor are they all necessary. More is not necessarily better. In addition be sure to find the appropriate measures of central tendency, the measures of dispersion, and the shapes of the distributions (for the quantitative variables) for the above data. Where appropriate, use the five number summary (the Min, Q1, Median, Q3, Max). Once again, use Excel as appropriate, and explain what the results mean. · Analyze the connections or relationships between the variables. There are ten possible pairings of two variables. Use graphical as well as numerical summary measures. Explain the results of the analysis. Be sure to consider all 10 pairings. Some variables show clear relationships, while others do not. Report Requirements · From the variable analysis above, provide the analysis and interpretation for three individual variables. This would include no more than 1 graph for each, one or two measures of central tendency and variability (as appropriate), the shapes of the distributions for quantitative variables, and two or three sentences of interpretation. · For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations. Please note that at least one pairing must include a qualitative variable and at least one pairing must not include a qualitative variable. · Prepare the report in Microsoft Word, integrating graphs and tables with text explanations and interpretations. Be sure to include graphical and numerical back up for the explanations and interpretations. Be selective in what is included in the report to meet the requirements of the report without extraneous information. · All DeVry University policies are in effect, including the plagiarism policy. · Project Part A report is due by the end of Week 2. · Project Part A is worth 100 total points. See grading rubric below. Submission: The report, including all relevant graphs and numerical analysis along with interpretations Format for report: A. Brief Introduction B. Discuss 1st individual variable, using graphical, numerical summary and interpretation C. Discuss 2nd individual variable, using graphical, numerical summary and interpretation D. Discuss 3rd individual variable, using graphical, numerical summary and interpretation E. Discuss 1st pairing of variables, using graphical, numerical summary and interpretation F. Discuss 2nd pairing of variables, using graphical, numerical summary and interpretation G. Discuss 3rd pairing of variables, using graphical, numerical summary and interpretation H. Conclusion Part B: Hypothesis Testing and Confidence Intervals Complete the following four hypotheses, using α = 0.05 for each. The week 5 spreadsheet can be used in these analyses. · 1. Mean sales per week exceed 42.5 per salesperson · 2. Proportion receiving online training is less than 55% · 3 Mean calls made among those with no training is at least 145 · 4. Mean time per call is 14.7 minutes · Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager's belief. Use the Eight Steps of a Test of Hypothesis from Section 9.1 of your text book as a guide. You can use either the p-value or the critical values to draw conclusions. Be sure to explain your conclusion and interpret that to the claim in simple terms · Compute 99% confidence intervals for the variables used in each hypothesis test, and interpret these intervals. · Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. · All DeVry University policies are in effect, including the plagiarism policy. · Project Part B report is due by the end of Week 6. · Project Part B is worth 100 total points. See grading rubric below. Format for report: A. Summary Report (about one paragraph on each of the four speculations) B. Appendix with the calculations of the Eight Elements of a Test of Hypothesis, the p-values, and the confidence intervals. Include the Excel formulas or spreadsheet screen shots used in the calculations. Final Project: Regression and Correlation Analysis Use the dependent variable (labeled Y) and one of the independent variables (labeled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following. The week 6 spreadsheet can be helpful in this work. 1. Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the "best fit" line. Interpret. 2. Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable. 3. Determine the correlation coefficient. Interpret. 4. Determine the coefficient of determination. Interpret. 5. Test the utility of this regression model by completing a hypothesis test of b=0 using α=0.10. Interpret results, including the p-value. 6. Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable. 7. Compute the confidence interval for b, using a 95% confidence level. Interpret this interval. 8. Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval. 9. Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval. 10. What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain. 11. Describe a business decision that could be made based on the results of this analysis. In other words, how might the business operations change based on these statistical results. 051015FrequencyBinHistogram of Calls (X1) Frequency y = 0,8569x + 122,9405010015020025001020304050607080Scatter Plot of Sales (Y) vs Calls (X1)y = 0,8569x + 122,9405010015020025001020304050607080Scatter Plot of Sales (Y) vs Calls (X1)