ECO XAM

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Eco 309 Exam 1 (Chapter 1 through 5) Class, You will have two hours to complete this exam once you have begun. You must download the data from doc sharing Exam 1 Data and copy it into Minitab. Do not try to upload, worksheets, tables or plots from Minitab or Excel into this exam. Select only the appropriate multiple choice answers in the exam. There is only one correct answer to each question. This exam must be completed and submitted by Saturday March 1 at 11:59 P.M. Central Time. I suggest that you complete the exam within one session to prevent the loss of your answers. You must take this exam since there will be no make-up tests. Stanley Holmes, Ph.D.

Question 1.1.

You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.

Quarter Seasonal Index Seasonally Adjusted Data

Q1 .80 295

Q2 .85 299

Q3 1.15 270

Q4 --- 271

(Points : 3)

325 225 252 271

Question 2.2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing? (Points : 3)

Alpha and Delta

Delta and Gamma

Alpha and Gamma

Std Dev and Mean

Question 3.3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient. (Points : 3)

Ho: r = .05 p < .5

Ho: r = 0 p >.05

Ho: r ≠ 0 p≤.05

Ho: r = 0 p≤.05

Question 4.4. In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable? (Points : 3)

The estimated value is 80% of the average monthly seasonal estimate. The estimate is .80 of the estimated Y trend value. The estimated value is .80 of the historical average CMA values. The estimated value has 20% more variation than the average historical Y data values.

Question 5.5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied? (Points : 4)

H1: u ≥ $1,368,000 A one-tailed t-test to the left. H1: u = $1,368,000 A two-tailed t-test. H1: u < $1,368,000 A one-tailed t-test to the left. H1: p < $1,368,000 A one-tailed test to the right.

Question 6.6. As the sample size from a population increases up to 30 observations, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value? (Points : 3)

The rejection region and the t-table value generally gets smaller. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

Question 7.7. You obtained autocorrelation LBQ value of 18.58 for the 12th lag from a data sample. Are the data significantly autocorrelated at the lag examined or not? You want to be 95% confident in your answer. (Points : 4)

Yes. The data are significantly correlated through the 12th lag. No. The data are not significantly correlated through the 12th lag.

No. Only the 12 lag period is not correlated.

You cannot tell since the number of sample observations is not provided.

The p-value is above .05 so the data is correlated.

Question 8.8.

The CEO of Lowes wants to see if city size has any relationship to the current profit margins of the company stores. What data type will he likely use to determine this?

(Points : 3)

Time series data of profits by store. Recent 10 year sample of profits by stores. Recent cross section of store profits by city. Trend of a random sample of store profits over time.

Question 9.9. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this? (Points : 3)

Type 2 error Autocorrelation error Type 3 error Type 1 error

Question 10.10. Do error measures indicate the statistical significance of forecast model residuals? (Points : 3)

Yes. They move in the same direction as statistical significance. Yes. As error measures decrease the variable significance increases. No They indicate only the magnitude of estimate error. No. They indicate only the statistical significance of a forecast or fitted values.

Question 11.11. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3rd previous period if the original alpha value is set at .8? (Points : 4)

The weight cannot be calculated since the data observation is not given. The weight is zero since the alpha value is set relatively high. .548 .0064

Question 12.12.

Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell? (This data also appears in the docsharing download for Exam 1 excel worksheet under the problem 12 tab.)

Ending Inv. Bal. Y		Monthly Sales X
1544		5053
1913		5052
2028		7507
1178		2887
1554		3880
1910		4454
1208		3855
2467		8824
2101		5716

(Points : 4)

Yes. The correlation coefficient is .873 that is greater than .05. Yes. The correlation p-value is .002 which is less than .05. No. The correlation coefficient is above the p-value. No. The correlation p-value is greater than the 95% confidence level.

Question 13.13. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random? (This data also appears in the docsharing excel worksheet download for Exam 1 under the Problem 13 tab.) Residuals

-24

-348

-892

-62

-378

-489

-342

490

578

198 (Points : 4)

Yes, since the residuals randomly vary in magnitude. Yes since the residuals are positive and negative and vary in magnitude. No, since the residuals are stationary and vary in magnitude. No, since the residuals indicate positive slope.

Question 14.14. Which form of exponential smoothing can result in a naïve forecast? A naïve forecast is one where the next forecast value is the same as the last observation. (Points : 3)

Winters with a very low seasonal coefficient.

Single with a very low trend coefficient.

Single with a very high alpha value. Double with a very low alpha value.

Question 15.15. A linear trend model is shown by Y = a + bX . In a perfectly stationary data series what value does b have?(Points : 3)

Zero. The X value. Mean/Std Dev. It cannot be determined since no data is shown.

Question 16.16. You are responsible for forecasting your company’s revenues for the next 24 months. You have three years of historical monthly data and previous forecasts that indicate that the company revenues with no obvious seasonality have grown significantly over that time. Which forecast method would you apply to the problem?(Points : 4)

3 period moving average 12 period moving average Simple exponential smoothing Double exponential smoothing

Question 17.17. You obtained a correlation coefficient from two data series that indicates a p-value of .97. Can you be 95% confident that the correlation is significantly different from zero? (Points : 4)

Yes, since the p value is above the confidence level. Yes, since the p value is above 1 minus the confidence level. No, since the p-value is above the 1 minus the confidence level. No, since the data is not provided to determine true confidence.

Question 18.18. Which of the hypotheses tests below are two-tailed?

1. A school administrator believes that recent TAKS test scores are above the national average.

2. A car dealer believes that the average value of used cars has changed since the recession. 3. A Texas state senator has taken a sample of his constituents that indicates their incomes are below the historical state average. The senator asserts that Texas incomes have fallen. (Points : 4)

All of the hypotheses are two-tailed. Only 3 is two-tailed. Only 2 is two-tailed. 1 and 3 are two- tailed.

Question 19.19. In decomposition the seasonal indices are the period relationships between what two data series? (Points : 3)

Seasonal moving averages and the trend data series. Smoothed data from centered moving averaging and the original data series. Trend data and the cycle factors. Trend data and the original data series.

Question 20.20. If sales growth and market penetration for a new product are expected to occur rapidly due to low product price and “need to have” technology which forecast model would you apply? (Points : 3)

Logistics S-curve Gompertz S-curve 3 period Moving Averages Double Exponential Smoothing

Question 21.21. Download the data for Exam 1 found in Doc Sharing (Exam 1 Data). Copy the excel data found on tab Problems 21 to 28 into Minitab to answer the remaining questions in this exam. Which exponential smoothing model is appropriate for this Sales data? (Points : 4)

Single Exponential Smoothing Double Exponential Smoothing (Holt's) Winter's Method Centered Moving Averages Linear Trend

Question 22.22. From the quarterly Kellogs sales data series in Doc Sharing select the best exponential smoothing model that applies? (This data appears in the Doc Sharing excel worksheet download for Exam 1 under the problem 21 through 26 tab.)

Run the data with the exponential smoothing model that applies and obtain the best model by adjusting each of the coefficients. (Do not take a hold out. Make sure that you only use one decimal place for each smoothing coefficient – e.g. .1, or .2, or .3 …. to .9) What is the forecast value for the future 4th quarter?

(Points : 4)

3639.48 3787.60 3538.32 3905.52

Question 23.23. What is the RMSE for the Fit period for the best exponential smoothing model? (Points : 4)

226.34 38.69 20.42 110.58

Question 24.24. Do the residuals have significant T, C or S through the 24th lag? (Points : 4)

Yes, since they still have significant seasonality. Yes, since they still have significant trend. No, there is no significant T, C or S. No, since none of the residual ACFs is significantly autoregressive.

Question 25.25. Use the same Kellogs quarterly sales data series and run a decomposition model and estimate four forecast periods. Which quarter has the greatest seasonal sales? (Points : 4)

Quarter 1 Quarter 2 Quarter 3 Quarter 4 All quarters are equall since there is no significant seasonality.

Question 26.26. What is the decomposition forecast value for the 4th period (last forecast month). Be sure to adjust the forecast with a cycle factor. (Points : 4)

3538.32 3212.39 3736.22 3627.45

Question 27.27.

Are the decomposition residuals random? Why or why not?

(Points : 4)

No. They still have seasonality. No. They still have significant cycle. Yes. They are normally distributed with a near zero mean. Yes. None of the residuals are significantly autoregressive.

Question 28.28. Based on MAPE and residual analysis, which method would you select to produce the best forecast? (Points : 4)

Decomposition since the distribution of residuals is more realistic and MAPE is about the same for both models. Exponential smoothing since the mean of the residuals is very close to zero and the mean absolute percent error is lower. Decomposition since the residual time series plot indicates that more seasonality has been picked up by the model and the MAPE is about the same for both models. Exponential smoothing and Decomposition are equally good since the MAPE is the same and the residuals for both methods are random.