1. A study was conducted by the State Transportation Department to determine whether a weigh-in-motion (WIM) scale could be used in place of the static scale currently used at port-of-entry(POE) locations across the state. The WIM scale weighs trucks as they drive over a scale, rather than making them stop at a POE to be weighed. It is thought that the mean speed of trucks crossing the WIM scale would be less that the posted speed limit of 65 miles per hour. Using the file Trucks on the CD-ROM:
   1. What conclusion can be reached concerning the preconception about the average speed at a significance level of .1? (2 points)
   2. A published report indicates that the WIM scale average truck length on the state highway exceeds 60 feet. Based on the sample data, can this claim be supported or refuted at a significance level of .05? (2 points)
   3. Create a new variable that represents the difference between the WIM gross weight and the POE gross weight. It is thought that if the WIM scale were effective that the average difference would be 0. Based on the sample data, what can be concluded at a significance level of .05? (3 points)
2. You are the Centenary college administrator and have been asked to take over the alumni capital campaign to raise money for the school. They want you to raise $3M so they can build a new floor onto the building in Parsippany. You discover a good source of data to use to build a linear regression model relating the amount of money expected to be received and the number of alumni at a school. The data is found on the file Penrose on the CD-ROM. You must develop and interpret the following information:
   1. Scatter Plot (1 point)
   2. Correlation Coefficient and test it at a significance level of .05 (1 point)
   3. Linear Regression Model ( show scatter plot and regression line) (2 points)
   4. Test the slope coefficient (that it is 0) at a significance level of .05 (1 point)
   5. Discuss the Standard Error of the Model (1 point)
   6. R-Squared value (1 point)
   7. Test for Positive Autocorrelation (Durbin Watson Statistic) (1 point)
   8. How many alumni do you predict will need to contribute for you to raise the $3M? Based on a 93% confidence interval for the slope, what is the average increase (confidence interval estimate) in money’s received from any 100 alumni? (2 points)
3. You have been hired by Car and Driver Magazine as a statistician and your job is to build a multiple regression model to predict the selling price of a new car based on the file Automobile on the CD-ROM. You can use all the variables except Company. You must use at least one of the 2 categorical variables, Car Type and ABS. (Hint: You will need to add dummy variables to your data file. Please make sure you create them correctly. ) Your model will be judged in terms of Adjusted R-Squared, F-Test, Individual variables significant, Standard Error, Autocorrelation and Multicollinearity. A summary sheet showing all your tests will be needed to prove that your model is good (You need to explain each of these). When you complete your model, produce a plot (and spreadsheet ) showing the actual price vs predicted price (based on your model) for each car in the data set along with the residuals (Actual price – Predicted price). (11 points)
   
   
4. Consider the following set of inventory data in thousands of dollars(000) for the 4 quarters in years 1997 to 2000:

1997 1998 1999 2000

1Q 209 218 215 230

2Q 195 203 210 227

3Q 215 226 220 238

4Q 208 220 216 235

1. Plot the data on a time scale, using first quarter of 1997=1, 2 ^nd quarter of 1997=2, etc. Based on your visual observations, what time series components are present? (2 points)
2. Determine the seasonal index for each quarter ( 1Q, 2Q, 3Q, 4Q). (2 points)
3. Convert the data to deseasonalized data and show the values for each quarter. (2 points)
4. Determine the trend line (write down the equation) for the deseasonalized data and plot it along with the deseasonalized data for years 1997 through 2000. Determine the MAD and MSE values for the trend data. (2 points).
5. Forecast the deseasonalized data for the year 200 1 using the model from part d and provide seasonal adjusted forecasts for each quarter of 2001 (Hint: Use the seasonal indexes you calculated in b). (2 points)

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Solution: The downloadable solution consists of 16 pages, 1379 words and 11 charts.
Deliverable: Word Document