1. (15 pts.) Chad Holms has been thinking about starting his own gasoline station. Chad has to decide on the size of the gas station. The annual profit will depend on both the size of the station and a number of marketing factors related to the oil industry and demand for gasoline. After careful analysis, Chad developed the following table.
Size of Gas Station Good Market Moderate Market Poor Market Maximum Minimum Equally Likely Expected Value
Small$270,000$150,000$80,000
Medium$300,000$230,000$30,000
Large$360,000$260,000-$180,000
Probability0.400.500.10
a- Complete the above table and identify best decisions (choices) under Maximax, Maximin, Equally Likely, and Hurwicz criterion.
Maximax Decision: Maximax Profit:
Maximin Decision: Maximin Profit:
Equally Likely Decision: Equally Likely Profit:
Expected Value Decision: Expected Value Profit:
Minimax Regret Decision: Minimax Regret Profit:
2- (45 pts.) Consider the monthly International Passenger totals (# of Pass. in 1000s) for an airline provided in the Excel file. Use Excel to perform following analysis.
a. Find the 3-month and 6-month moving averages for all data values and find all forecast and forecast for February 2024. Find MAD for both forecasts and determine the best moving average forecast.
b. Find the three-month weighted moving average forecasts and find all forecasts and forecast for February 2024 if weights of 0.2, 0.3, and 0.5 are used with highest weights assigned to the latest months. Find MAD and compare with MADs in part (a). Is the weighted MA forecast better than simple moving averages in part a?
c. Use the exponential moving average to find all forecasts and the forecast for February 2024 Assume forecast of 500 for January 2014 and =0.70. Find MAD and compare to MAD values in parts (a and b).
d. Construct a linear trend line graph of # of Passengers (use smooth line graph option), insert the equation of the best linear fitted line and the R-squared value. Discuss findings (time series components) based on graph.
e. Find monthly seasonal relatives (indices) and construct a column of de-seasonalized values for # of Passengers by dividing monthly number of passengers by respective seasonal monthly indices.
f. Construct a trend linear line graph of De-seas # of Passengers line (use smooth line graph option), insert the best linear fitted line and R-squared. Discuss findings based on graph, equation, and R2. Is this model a better fit compared to model in part (d). Explain why?
g. Use the linear trend line equation model in part f to find forecasts for February to May 2024 and seasonalize forecasts by multiplying by respective monthly seasonal indices obtained in part (e).
3. (40 pts.) Consider the real estate data on 60 homes in a middle-class neighborhood of Southwest Houston provided on the Excel data file. The variables are:
Price (Y) in $1000, Square Feet (X1), # of Rooms (X2), # of Bedrooms (X3), # of Bathrooms (X4), Age (X5)
a. Construct Scatter plot of all 5 variables (one at a time) vs. Price (Y) (5 graphs), insert best fitted linear equations and comment on the goodness of the fit based on R-squared values.
b. Construct the correlation matrix of all 6 variables and rank variables based on absolute values correlations with Price. Discuss correlation of variables against Price in plain language.
c. Construct a full model using all independent variables vs. Price (Y), find the equation, R-squared, significant F, and comment on the goodness of the model. Rank the independent variables based on degree of contribution to the model based on their P-values.
d. Based on independent variable ranking in part C, select 4 best variables and construct 4 variable multiple linear regression model to predict Price. Make sure to obtain residual values in the model. Outline the regression equation, R-squared, significant F, and comment on the goodness of the model. Make sure to interpret R-Squared and Significant F values.
e. Use the residuals output in part (d) and identify top 5 overvalued and 5 undervalued homes in this neighborhood.
f. Based on model in part (d), estimate the value for 4000 sq. ft. home with 6 rooms, 3.5 baths, 4 bedrooms, and age of 20.
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