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Format: You must submit your project report in a single file through Canvas. The acceptable formats are Microsoft Word (*.xlsx) or PDF (*.pdf) – no exceptions. The submission page is in the Semester Project module. Projects submitted in multiple parts, in a format other than Word or PDF, or via email/hardcopy will be rejected. Style Requirements: The Semester Project module contains a sample project that would receive a 100% grade. Your report should be formatted similarly. −The first page of your report must be a title page containing your name, the course and section number, the title "Semester Project," and the submission date. −Use a font suitable for an official business document. Any standard typeface is acceptable as long as it is readable and presents a professional appearance (Calibri and Times New Roman are good examples, but not the only possibilities). The size should be no smaller than 12 point, and the color should be black. −Do not include any borders, decorative images/illustrations, or watermarking.−Embed all graphics directly into your project file. I will not accept separate files containing graphics.Data Set: All students will use the same data set: Spring 2021 Semester Project Raw Data. The data set is located in the StatCrunch MTH 245 Assignments Group. The data come from the real estate listings of 521 recently sold homes in a suburban Pennsylvania county. The

variables of interest are SqrFeet( usable floor space in square feet) and SalePrice (the sale price in thousands of U.S. dollars). Technology Requirements: Except where required to build graphs or charts, all numerical calculations must be performed using StatCrunch. Do not use a graphing calculator, Excel, standard normal tables, or any other method for your numerical calculations.Graphics Requirements: All graphics must be constructed using StatCrunch, Excel, or other computer-based graphics program. Hand-drawn plots, cell phone pictures of graphics, etc., are not acceptable. All graphics must include an informative title and (except for boxplots) correct labels for both axes. Orient all boxplots horizontally.Rounding Rules:−In Section 1, all upper and lower class bounds for the SqrFeet histogram should be integers, and the upper and lower class bounds for the SalePrice histogram should berounded to one decimal place. −In Section 2, do not round the five-number summaries. −Round all other sample statistics in Section 2, as well as the confidence limits in Section 3, to one decimal place for SqrFeet and two decimal places for SalePrice. −Round the two p-values—one each in Sections 4 and 5—to three decimal places.−In Section 5, round the regression coefficients to one decimal place and all othercalculated values (besides the p-values) to two decimal places.−Add trailing zeroes to any rounded value as needed.−Do not simply paste screen shots of StatCrunch output into your report.−Warning: do not use the sample project as an example of how to round! The data set used in that particular project is different from yours, so the values are all rounded differently!Required Content: Organize your report in five separate sections using the following numbers and titles. The required elements for each section are as follows:Section 1 – Visual Data Assessment. Create a histogram for each variable of interest: SqrFeetand SalePrice. For SqrFeet, use a "Start at:" value of 900 and a "Width:" value of 350; for SalePrice, use a "Start at:" value of 50 and a "Width:" value of 50. It is not necessary to display frequency counts above the bars. For each histogram, include a paragraph that answers each of the following questions: a.Is the histogram symmetric, left-skewed, right-skewed, or uniform?b.How many peaks does the histogram have, and in which class(es) are they located(must include the correct lower and upper bounds for each class listed)? c.Does the histogram have any gaps between classes? If so, where are they?

Section 2 – Descriptive Statistics.a.For each variable, find the mean, range, variance, standard deviation, and five-number summary. Display these numbers in a format that is easy to understand. (Do not simply copy screencaps of the StatCrunch output!)b.Construct a regular boxplot for each variable. For each boxplot, include a brief statement containing an assessment of whether the data appear to be symmetric, left-skewed, right-skewed, or uniform. c.For each variable, construct a modified boxplot and use it to identify potential outliers. I f any exist, list them by value; if none exist, say so. Section 3 – Confidence Intervals. Construct a 95% confidence interval for the meanμ of each variable (two intervals total). Use algebraic format for each interval (𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙<𝜇𝜇<𝑢𝑢𝑢𝑢𝑢𝑢𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙). State the distribution you used for each interval (𝑙𝑙 or normal). Section 4 – Hypothesis Test. Using the p-value method, conduct a formal hypothesis test of the claim that 𝜇𝜇, the mean of SalePrice, is greater than 265. Use𝛼𝛼=0.01. Include the following in your written summary of the results:a.Your null and alternate hypotheses in the proper format using standard notation. b.The type of distribution you used (𝑙𝑙 or normal).c.The p-value and its logical relationship to 𝛼𝛼 (≤ or >). d.Your decision regarding the null hypothesis: reject or fail to reject.e.A statement interpreting your decision: reject/fail to reject (or support/fail to support) the original claim that the mean of SalePrice is greater than 265. Note: Section 4 only applies to SalePrice. There is no hypothesis test related to SqrFeet. Section 5 – Correlation/Regression Analysis.a.Construct a linear regression model with SqrFeet as the predictor and SalePrice as the response. State the equationin correct algebraic format as shown in the course notes.b.Create a scatter plot of the data with a plot of the least squares line included. (StatCrunch should generate this when you calculated the model in 5a.) The plot must include an informative title and correct labels for both axes. c.Use the coefficient of determination to identify the percentage of the variation in SalePrice explained by the variation in SqrFeet. d.Identify all likely influential points (all points with Cook's Distance greater than 1.0). If any exist, list them as ordered pairs in the form (SqrFeet, SalePrice). If none exist, say so.

e.Conduct a formal hypothesis test at 𝛼𝛼=0.05 to determine if there is sufficient evidence of correlation between SqrFeet and SalePrice. Include the following: 1) The p-value and its logical relationship to 𝛼𝛼 (≤ or >). 2)Your decision regarding the null hypothesis: reject or fail to reject. 3)A statement regarding the sufficiency of the evidence for a linear relationship between SqrFeet and SalePrice. f.State whether the equation in 5a satisfies the following LINE criteria (assume the residuals are independent): Linear Relationship (L):Using the scatterplot with fitted line, determine if a linear model is appropriate based on the model's visual fit to the data. Normally-Distributed Residuals (N): Determine if the residuals fit a normaldistribution using a residual histogram and a Q-Q plot. (Do not use a boxplot.)Equal Variances of the Residuals (E): Assess the residuals for constant variance using a plot of the residuals versus SqrFeet. g.Verify your assessment of the N criterion in 5f by conducting a goodness-of-fit test for normality on the model residuals. Use 𝛼𝛼=0.05. Report the p-value, its logical relationship to 𝛼𝛼 (≤ or >), and your interpretation of the result.h.Use the results from 5e, 5f, and 5g to determine if the model you built in 5a provides valid estimates of SalePrice as a function of SqrFeet. Justify your decision.i.Provide a valid estimate of 𝑦𝑦𝑛𝑛𝑛𝑛𝑛𝑛, a new observation of SalePrice for a home where SqrFeet =2,500. Use either the regression model you constructed in 5a or calculate the value using the SalePrice data column by itself, whichever is appropriate. j.If you use the regression model from 5a to calculate the estimate in 5i, calculate a 95% prediction interval estimate of 𝑦𝑦𝑛𝑛𝑛𝑛𝑛𝑛. If the model in 5a is invalid, include a statement that a prediction interval estimate is not applicable.