CompetencyDetermine and interpret the linear correlation coefficient, and use linear regression to find a best fit line for a scatter plot of the data and make predictions.ScenarioAccording to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.Concept being StudiedCorrelation and regressionCreating scatterplotsConstructing and interpreting a Hypothesis Test for Correlation using r as the test statisticYou are given a spreadsheet that contains the following information:Magnitude measured on the Richter scaleDepth in kmUsing the spreadsheet, you will answer the problems below in a PowerPoint presentation.What to SubmitThe PowerPoint presentation should answer and explain the following questions based on the spreadsheet provided above.Slide 1: Title slideSlide 2: Introduce your scenario and data set including the variables provided.Slide 3: Construct a scatterplot of the two variables provided in the spreadsheet. Include a description of what you see in the scatterplot.Slide 4: Find the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Include an explanation on how you found those values.Slide 5: Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain.Slide 6: Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.Slide 7: Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0? Include the correct units.Slide 8: Conclude by recapping your ideas by summarizing the information presented in context of the scenario.Along with your PowerPoint presentation, you should include your Excel document which shows all calculations.

The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast.B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers two analysis packages: one based on a sample size of 100 listings, and another based on a sample size of 1,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 1,000 listings than for the package with 100 listings.Sample size of 100 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $25,000Cost for service to B&K: $2,000Sample size of 1,000 listings:95% confidence interval for the mean of the Northeast house listing price has a margin of error of $5,000Cost for service to B&K: $10,000The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K.In other words, which option is preferable?Spending more on data collection and having a smaller margin of errorSpending less on data collection and having a larger margin of errorChoosing an option somewhere in the middleFor your initial post:Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for both packages. “I am [#] % confident the true mean . . . [in context].”Explain the factors that went into your recommendation, including a discussion of the margin of error