CompetenciesIn this project, you will demonstrate your mastery of the following competencies:Apply statistical techniques to address research problemsPerform regression analysis to address an authentic problemOverviewThe purpose of this project is to have you complete all of the steps of a real-world linear regression research project starting with developing a research question, then completing a comprehensive statistical analysis, and ending with summarizing your research conclusions.ScenarioYou have been hired by the D. M. Pan National Real Estate Company to develop a model to predict median housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the median housing prices based square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.DirectionsUsing the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator for what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate County Data spreadsheet (both found in the Supporting Materials section) for your statistical analysis.Note: Present your data in a clearly labeled table and using clearly labeled graphs.Specifically, include the following in your report:IntroductionDescribe the report: Give a brief description of the purpose of your report.Define the question your report is trying to answer.Explain when using linear regression is most appropriate.When using linear regression, what would you expect the scatterplot to look like?Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.Data CollectionSampling the data: Select a random sample of 50 counties.Identify your response and predictor variables.Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.Data AnalysisHistogram: For your two variables, create histograms.Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.Interpret the graphs and statistics:Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.Compare and contrast the shape, center, spread, and any unusual characteristic for your sample of house sales with the national population. Is your sample representative of national housing market sales?Develop Your Regression ModelScatterplot: Provide a graph of the scatterplot of the data with a line of best fit.Explain if a regression model is appropriate to develop based on your scatterplot.Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.Identify any possible outliers or influential points and discuss their effect on the correlation.Discuss keeping or removing outlier data points and what impact your decision would have on your model.Find r: Find the correlation coefficient (r).Explain how the r value you calculated supports what you noticed in your scatterplot.Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.Interpret regression equation: Interpret the slope and intercept in context.Strength of the equation: Provide and interpret R-squared.Determine the strength of the linear regression equation you developed.Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the square footage of your home.ConclusionsSummarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.Did you see the results you expected, or was anything different from your expectations or experiences?What changes could support different results, or help to solve a different problem?Provide at least one question that would be interesting for follow-up research.

Task 1Find a local building and estimate its height. How tall do you think the building is?The smallest building in town is about 50 ft. high. Use the Internet to find some initial velocities for different types of fireworks. What are some of the initial velocities that you foundSome have a Vi of 39.2 m/s, 152 m/s, etc. Task 2 1. While setting up a fireworks display, you have a tool at the top of the building and need to drop it to a coworker below. How long will it take the tool to fall to the ground? (Hint: use the first equation that you were given above, h(t−) = 1+6t2 h0 . For the building’s height, use the height of the building that you estimated in Task 1.)h = 50 feet-50= -16t^2 – 0t=1.767767 Draw a graph that represents the path of this tool falling to the ground. Be sure to label your axes with a title and a scale. Your graph should show the height of the tool, h, after t seconds have passed. Label this line “Tool”. State whether the parabola represented by h(t−) = 1+6t2 250t opens up or down. Explain why your answer makes sense in the context of this problem. One of the fireworks is launched from the top of the building with an initial upward velocity of 150 ft/sec. -What is the equation for this situation? -When will the firework land if it does not explode? -Make a table for this situation so that it shows the height from time t = 0 until it hits the ground. -Calculate the axis of symmetry. -Calculate the coordinates of the vertex. -Explain why negative values for t and h(t) do not make sense for this problem. -On the same coordinate plane from #1, draw a graph that represents the path of this firework. Make sure that your graph is labeled appropriately. Label this graph “Firework #1”. -Choose an initial velocity for a firework based on your research from Task 1 Write an equation that represents the path of a firework that is launched from the ground with the initial velocity that you chose. Suppose this firework is set to explode 3 seconds after it is launched. At what height will this firework be when it explodes? On the same coordinate plane that you have been using, draw a graph that represents the path of this firework. Mark your graph to indicate the point at which the firework will explode. Label this graph “Firework #2”. You launch a third firework. Decide whether you want to launch it from the ground or from the roof of the building. Also, choose a height at which this firework will explode and an initial velocity for this firework. How long after setting off the firework should the delay be set? On the same coordinate plane that you have been using, draw a graph that represents the path of this firework. Mark your graph to indicate the point at which the firework will explode. Label this graph “Firework #3”. What can you conclude about how the height of the building and the initial velocity of the item launched affect the maximum height and the time it takes to get there? Task 3You will submit the following items.• results of your research, including the height of the building that you found and initial velocities for fireworks a graph that shows the paths of the tool that was dropped and the three fireworks that were launched