Answer the following questions.
1. In 1990 Congress passed the Oil Pollution Act requiring tankers to have thicker hulls to prevent oil spills. Data were collected on 42 major oil spills recording the spillage amount (in thousands of metric tons) and the cause of the puncture (included in the Oilspill Excel file posted on Canvas). (16 points total)
a. A researcher is interested in determining whether grounding accidents and hull failures result in different spillage. Is there a difference in the mean spillage amount for spills caused by grounding accidents and spills caused by hull failures? Conduct any relevant six-step hypothesis tests to answer part b. (12 points total)
. Fully explain how you decided which MS Excel tool(s) to use to a
ive at your answer to this question. (4 points)
2. You work for a supermarket that is considering the best way to promote sales of its store-
and canned vegetables. Store managers believe allocating additional shelf space to the store-
and canned vegetables would create additional sales. Company executives, on the other hand, believe increasing advertising expenditures would be a more effective strategy to expand sales. Complete a regression analysis to help answer this question (use the CANVEG Excel file posted on Canvas). NOTE: consider three possible specifications for modeling: simple linear model, a multiple linear regression model, or an interaction model. (34 points total)
As you consider the alternative specifications of the model, include all results in the Excel spreadsheet you submit. Be sure your Excel results are very clearly labeled so your results that support your final answers to the following questions can be differentiated from the supporting documentation in Excel of the other model specifications. You do NOT need to answer questions a-h for all of the model specifications you consider, but you might find these questions helpful in selecting the model you recommend based on the data. You DO need to answer questions a-h for the final model you recommend. Question i should justify your selection of the final model relative to the other model specifications. You might find it helpful to read through all of the following questions, especially part i, before you begin working in Excel.
a) Write out the equation that represents the hypothesized population regression equation for the model you select as the one that best answers the underlying question (3 points).
) Explain whether a positive or negative relationship is hypothesized between the variables (2 points).
c) Use the “Microsoft Excel Data Analysis Toolpak” to determine the regression coefficients for the relationship and write out the final estimated regression equation for the model you selected. (4 points) You must include the MS Excel output.
d) Give a practical interpretation of the slope(s) of the least squares line (be specific! 4 points).
e) Over what range of x-values is the interpretation meaningful? (1 point)
f) Does the estimated slope support the relationship between the two variables you initially hypothesized (in parts a and b)? Explain. (1 point)
g) Evaluate the overall utility of the model including any relevant hypothesis tests (be sure to fully write all 6-steps of any hypothesis test conducted, you can specify the rejection region in words it is not necessary to include a graph though you can if you prefer to). (6 points)
h) Include any hypothesis tests of individual coefficients that are appropriate given your choice of model specification and results. (3 points)
i) Given all of the results for the alternative specifications, what is your response to the company about pursuing expanding shelf space and/or increasing advertising expenditures? Prepare a BRIEF explanation of the results of your analysis. This explanation should be written in a professional manner as if you were writing a summary of the results for a reader who is at least familiar with the basics of regression analysis (paragraph form is fine, it does not need to be prepared as a “memo” or “report”). It is NOT sufficient to simply refer to the numeric values of your regression results, you must explain how the results support your recommendation and what you considered in selecting your final model. (You should specifically reference your regression results AND compare the parts of your regression analysis to other model specifications you considered if doing so facilitates your explanation, but be sure to address how they support your recommendation.) (10 points total)