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For this project you will need to apply simple linear regression and study a problem of interest. In this project, you will perform a statistical analysis to investigate how two quantitative variables (not qualitative variables) are associated and how one influences the other. You can choose what two variables you are interested in studying and will collect your own data in order to perform an analysis. I will provide you with a few good sources from which you might be interested in collecting your data. The requirements for this project are discussed in detail below. Use of Excel or other computer statistical software will be required to carry out various calculations, produce tables and graphs, and to perform a statistical analysis. You will be required to write a 2.5 to 3 page report (double-spaced) briefly discussing the problem being studied, your analysis and findings, as well as additional or concluding remarks. Note that the 2 to 3 page minimum length does not include any tables or graphs (which should be included separately with the paper). You will need to provide the Excel graphs or charts produced along with the report, as well as the raw data collected. The report section of the project needs to be well-written with good sentence structure and proper grammar. You must include an introduction and a strong conclusion, as outlined in the requirements below: A. Requirements for the Written Report (Minimum 2.5-3 pages, double-spaced) a) An introduction paragraph discussing the problem being studied, some background on the topic, and why it is of interest to you. Mention how your data was obtained and cite your source. b) Describe somewhere which variable would be the explanatory variable and which one is the response variable, and why so. c) Interpret the meaning of the correlation coefficient in context of the problem and what this means. d) Include the linear regression equation in the report with the determined intercept and slope values. Also, interpret the slope and intercept values. Lastly, for a particular chosen value of the explanatory variable predict what the response variable would be and interpret what this would mean in a sentence. (Make sure the explanatory variable value chosen would make sense for this problem) e) Find what the coefficient of determination value is, and interpret it in the context of this problem being studied. Does this indicate that the model is a good fit for the data and why? f) Discuss, based on your findings, if there is a significant linear relationship between the two variables. g) Perform diagnostics on the regression model using residual plots. Using these, comment on whether or not a linear model should be appropriate, on whether or not the residual error term appears to have constant variance, and on whether or not there are any outliers. h) Briefly describe, in conclusion, if this regression model does a good job in explaining the dataset, based on your Excel findings. Here you can also make additional comments about the regression model that you think are worth mentioning. This is your chance to be creative and provide additional insight. B. Requirements for the Appendix After the Written Report: a) A scatter diagram showing the relationship between the 2 variables being analyzed. Include a graph of the linear regression equation in this plot as well. Be sure to label the axes and the plot. b) Show the tables, determined using Excel toolbars and functions, which display coefficient values, t values for the regression coefficients, and the p-values. c) The residual plot, as shown in class. Be sure to label the axes and the plot. d) The raw data collected. e) Describe how you and your group member each contributed to the project. Please no plagiarism, as it will be checked when submitted. Thank you!
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