A mini project.
Statistics Eric Smith Mini-Project 1 Anscombe’s Quartet In 1973, the statistician Francis Anscombe constructed four data sets with some interesting properties, which you will explore in this project. Dr. Anscombe’s purpose was to demonstrate both the importance of graphing data before analyzing it and the effect of outliers and other influential observations on statistical properties. A variation of Dr. Anscombe’s collection of data sets is given in the table on the second page of this document. Use the following headings for your project submission: • Summary Statistics (4 points) Use technology to find the correlation coefficient and the regression line for each data set. Round each value (correlation coefficient, slope, and y-intercept) to two decimal places. In your project submission, indicate what technology and what function you used (for example: “We used LinReg on a TI-83+ calculator,” or “We used the CORREL, SLOPE, and INTERCEPT functions in Excel.”). You should notice something interesting about the results of the correlation coefficients and regression lines! • Scatter Plots (4 points) Use technology to construct a scatter plot for each data set. Include the regression line in each scatter plot. • Differences (4 points) Discuss the differences between the data sets that are not detected by the summary statistics, but are shown by the scatter plots. • Predictions (4 points) For each data set, decide whether it would be appropriate to use the regression line to predict the value of y when x = 19, and explain why it would or would not be appropriate. If it is appropriate, calculate the predicted value of y, accurate to two decimal places. Overall Presentation (4 points) The remaining 4 points will be based on the overall presentation of your project, including but not limited to: • Explanations are clear and complete. • Correct use of mathematical notation and terminology. • An introduction is included that clearly explains the goal and context of the project. Statistics Eric Smith Mini-Project 1 Anscombe’s quartet I II III IV x y x y x y 14 16.08 14 18.28 14 14.92 15.8 13.16 15.8 13.9 15.8 16.28 15.8 13.54 15.8 11.52 11.3 15.16 11.3 17.48 11.3 25.48 15.8 15.42 14.9 17.62 14.9 17.54 14.9 14.22 15.8 17.68 13.1 16.66 13.1 18.52 13.1 15.62 15.8 16.94 10.4 19.92 10.4 16.2 10.4 17.68 15.8 14.08 17.6 14.48 17.6 12.26 17.6 12.16 15.8 10.5 19.4 19.4 19.4 10.78 5.9 25 8.52 6.2 x y 12.2 21.68 12.2 18.26 12.2 16.3 15.8 11.12 16.7 16.7 14.52 16.7 12.84 15.8 15.82 18.5 18.5 11.46 15.8 13.78 9.64 18.5 11.36 9.48
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