Business Stats

BUS 305 Name ______________________________

Make Up Exam 2 70 points

General Instructions: This is an open book, open notes, laptop exam. You may use your laptop for any problem, but some problems require that you do direct calculations. Show your work; problems without sufficient documentation may not receive full credit even if answers are correct. All students are expected to abide by the Code of Student Conduct. Do not use more decimal places than are needed (certainly no more than four in any answer).

1. (10 points) Trend Analysis

Use the data shown on the Problem 1 tab to create a linear trend model and forecast the value for period 25.

The intercept of the model is ______________ The slope of the model is _______________

The forecast for period 25 is _______________

From a statistical standpoint, can it be concluded that this time series is not flat but does indeed have a trend? Explain, using supporting evidence from the output.

2. (15 points) Use software to create a multiple regression model to predict a manager’s salary (in $000’s) based on years of experience, number of staff supervised, and whether or not the manager has an advanced degree (1 = yes, 0 = no). The data for this problem is in the associated Excel file on the Problem 2 tab.

a. Write the equation of the regression line. Use notation, not words, for the variables.

b. What salary would this model predict for an employee with 8 years of experience, who supervises 10 staff, and has an advanced degree?

c. What average effect on expected salary does this model attribute to having the advanced degree?

d. Are all of the variables statistically significant? Explain.

3. (10 points) The regression output shown below is from a model where the mileage (in 000’s of miles) and condition (from 1 – 5, with 5 being the best) of used cars are used to explain their price (in $000’s).

a. Write the equation of the estimated regression line.

b. What price would this model predict for a car with 80,000 miles and a condition level 3?

c. To make this model better, we might include other explanatory variables. If we were to include the original list price of the car as an X variable, would you expect the sign on the regression coefficient to be positive or negative? State which, and explain.

4. (10 points) Use the time series in the associated data file to create the naïve forecasts. Remember, the naïve forecast for one period is the actual value from the previous period. There is no forecast for time period 1. Use your results to answer the questions below. The data appears on the Problem 4 tab.

a. Report the forecast, the error, the absolute error, the squared error, and the absolute percent error for time period 10.

Forecast = _____________Error = __________ Absolute error = ___________

Squared error = ­___________ Absolute percent error = _______________

b. Calculate the three error measures for your forecasts.

The MAD = ________________

The MSE = ________________

The MAPE = ________________

c. The forecaster for a giant corporation has developed one model to predict total quarterly corporate sales, and another model to predict the number of store managers in the company who will be promoted to district managers each year. She thinks that MAPE would be the best error measure to determine which model worked better.

Do you agree that MAPE is better than MAD or MSE? Explain why or why not.

5. (10 points) Exponential Smoothing

Using alpha = 0.2, prepare simple exponential smoothing forecasts for the time series in the associated data file on the Problem 5 tab. Report here your forecasts for times 9 and 10. Round results to 4 decimal places.

The predicted value for time 9 = ______________

The predicted value for time 10 = ______________

In general, to create forecasts that react very quickly to changes in the actual values, does a high or a low value of alpha work better?

6. (15 points) A seasonal decomposition procedure yielded the information shown below:

Trend equation Trend = 1217 – 2.1t

Seasonal Indexes: S1 = .82 S2 = 1.14 S3 = .95 S4 = 1.09

Time was originally recorded for quarter 1 of year 1. Use this information to find the final forecast for the four quarters of year 3. Use the extra columns any way you wish.

The actual value for the third quarter of year 2 was 1180. What is the deseasonalized value for this actual observation?