Question 1

In a time series with quarterly sales data,assume that the seasonal index for the summer quarter has been found to be 0.87,this can be interpreted to mean that sales tend to be 87 percent higher in the summer quarter when compared to the other quarters.

Accepted Answer

The seasonal index of 0.87 for the summer quarter does not mean that sales are 87% higher in the summer quarter compared to the other quarters. It means that the sales in the summer quarter are estimated to be 13% lower than the average sales for all quarters. This is because the seasonal index is calculated by taking the average sales for the summer quarter and dividing it by the average sales for all quarters. Therefore, the correct interpretation would be that sales in the summer quarter tend to be 13% lower than the average sales for all quarters.

Question 2

In using simple linear regression to find the linear trend in an annual time series from 1990 to 2005,the values 1990,1991,etc.are used as the values of the independent variable t when the regression is conducted.

Accepted Answer

The answer of In using simple linear regression to find...

Question 3

The Baker's Candy Company has been in business for three years.The quarterly sales data for the company are shown as follows:
  Based on these data,the seasonal index for quarters 3,7,and 11 is approximately 1.61

Accepted Answer

The answer of The Baker's Candy Company has been in...

Question 4

You are given the following linear trend model: F_t = 345.60 - 200.5(t).This model implies that in year 1,the dependent variable had a value of 145.1.

Accepted Answer

The model implies that in year 1 (t=1), the dependent variable F_t would be 345.60 - 200.5(1) = 145.1, which is correct. However, the statement is false because it incorrectly implies that the model itself states the value, rather than the calculation based on the model.

Question 5

One of the disadvantages of a regression-based linear trend forecasting model is that the forecast errors are computed for time periods that were used in developing the forecasting model and thus do not truly measure the forecasting ability of the model.

Accepted Answer

This is because the model uses past data to predict the future, and thus the errors are measured for the data that was already used in developing the model. It does not reflect the model's ability to predict new, unseen data in the future.

Question 6

In measuring forecast errors,the MAD and the square root of the MSE will provide similar (but not identical)values,in that both provide a measure of the "typical" amount of error in forecasts.

Accepted Answer

MAD (Mean Absolute Deviation) and the square root of MSE (Mean Squared Error) are both measures of the average amount of error in forecasts. While they may provide slightly different numerical values, they serve the same purpose in evaluating forecast accuracy.

Question 7

Gibson,Inc.is a holding company that owns several businesses.One such business is a truck sales company.To help in managing this operation,managers at Gibson have collected sales data for the past 20 years showing the number of trucks sold each year.They have then developed the linear trend forecasting model shown as follows:  Based on this information,it appears that the time series has a strong positive linear trend component.

Accepted Answer

The given linear trend forecasting model shows a positive slope, indicating a strong positive linear trend component in the sales data. Therefore, the statement is true.

Question 8

Renton Industries makes replacement parts for the automobile industry.As part of the company's capacity planning,it needs a long-range total demand forecast.The following information was generated based on 10 years of historical data on total number of parts sold each year.  Based on this information we can conclude that the linear trend model explains a significant proportion of the variation in the number of parts sold,because the p-value is much smaller than any reasonable α that we might use.

Accepted Answer

The statement is true because a small p-value indicates that it is unlikely that the observed variation is due to random chance alone, and therefore we can conclude that the linear trend model is a good fit for the data.

Question 9

A plot of the time series with time on the horizontal axis is an effective means of assessing whether the series is linear or nonlinear.

Accepted Answer

A plot of the time series with time on the horizontal axis can visually show patterns and trends, making it easier to determine if the series is linear or nonlinear. A straight line would indicate linearity, while a curved or erratic line would suggest nonlinearity.

Question 10

The Baker's Candy Company has been in business for three years.The quarterly sales data for the company are shown as follows:
  As a first step in computing a seasonal index,the four-period moving average corresponding to the mid-point between periods 2 and 3 is 3,350.

Accepted Answer

The answer of The Baker's Candy Company has been in...

Question 11

Gibson,Inc.is a holding company that owns several businesses.One such business is a truck sales company.To help in managing this operation,managers at Gibson have collected sales data for the past 20 years showing the number of trucks sold each year.They have then developed the linear trend forecasting model shown as follows:  Based on this information,the fitted value for year 1 is about 99.

Accepted Answer

The answer of Gibson,Inc.is a holding company that owns several...

Question 12

Forecast bias measures the average amount of error per forecast,so a positive value means that forecasts tended to be too low.

Accepted Answer

This is correct. A positive forecast bias indicates that the forecasts were too low on average.

Question 13

In comparing two or more forecasting models,the MAD value is useful in determining how successful the models were in fitting historical data.

Accepted Answer

MAD (Mean Absolute Deviation) is a measure of the difference between the actual values and the forecasted values in a time series. It is a commonly used metric to compare the accuracy of forecasting models. The lower the MAD value, the better the model can fit historical data. Therefore, MAD is useful in determining how successful the models were in fitting historical data.

Question 14

It is possible to use linear regression analysis to develop a forecasting model for nonlinear data if we can effectively transform the data.

Accepted Answer

By applying appropriate transformations, nonlinear data can be made linear, and linear regression can be applied to develop a forecasting model.

Question 15

A seasonal index is a statistic that is computed from time-series data to indicate the effect of the seasonality in the time-series data.

Accepted Answer

A seasonal index is used to measure the seasonal variation in time-series data. It is calculated by dividing the average value of a specific time period by the overall average of the entire time series, and multiplying the result by 100. This provides a percentage value that indicates the degree to which a particular time period is above or below the overall average. The seasonal index can be used to adjust for the seasonal fluctuations in data to provide a more accurate representation of trends and patterns in the data.

Question 16

The reason for using split samples in developing a forecasting model is to eliminate the potential for bias in the resulting model.

Accepted Answer

The answer of The reason for using split samples in...

Question 17

The Baker's Candy Company has been in business for three years.The quarterly sales data for the company are shown as follows:
  Based on this information,the data reflect both a linear trend and seasonal components.

Accepted Answer

The answer of The Baker's Candy Company has been in...

Question 18

Renton Industries makes replacement parts for the automobile industry.As part of the company's capacity planning,it needs a long-range total demand forecast.The following information was generated based on 10 years of historical data on total number of parts sold each year.  Based on this information,the percent of variation in the number of parts sold that is explained by the linear trend model is approximately 90.9.

Accepted Answer

The statement says that "the percent of variation in the number of parts sold that is explained by the linear trend model is approximately 90.9", which means that the linear trend model is a good fit for the historical data and can explain a significant proportion of the variation in the number of parts sold. Therefore, the answer is True, option A.

Question 19

Renton Industries makes replacement parts for the automobile industry.As part of the company's capacity planning,it needs a long-range total demand forecast.The following information was generated based on 10 years of historical data on total number of parts sold each year.  Based on this information,we can conclude that sales on average have been growing by more than 48 thousand annually.

Accepted Answer

Looking at the trend line in the graph, we can see that there is a positive slope indicating an increase in sales over time. Additionally, the slope of the trend line is greater than 48 thousand, indicating that sales on average have been growing by more than 48 thousand annually.

Question 20

From an annual time series of a company's sales the linear trend model F_t = 127 + 54(t)has been developed.This means that on average sales have been increasing by 127 per year.

Accepted Answer

The linear trend model indicates that sales have been increasing by 54 units per year, as 54 is the coefficient of the time variable t, representing the average annual increase.

Quiz 16: Analyzing and Forecasting Time-Series Data

In a time series with quarterly sales data,assume that the seasonal index for the summer quarter has been found to be 0.87,this can be interpreted to mean that sales tend to be 87 percent higher in the summer quarter when compared to the other quarters.

In using simple linear regression to find the linear trend in an annual time series from 1990 to 2005,the values 1990,1991,etc.are used as the values of the independent variable t when the regression is conducted.

The Baker's Candy Company has been in business for three years.The quarterly sales data for the company are shown as follows: Based on these data,the seasonal index for quarters 3,7,and 11 is approximately 1.61

You are given the following linear trend model: Ft = 345.60 - 200.5(t).This model implies that in year 1,the dependent variable had a value of 145.1.

One of the disadvantages of a regression-based linear trend forecasting model is that the forecast errors are computed for time periods that were used in developing the forecasting model and thus do not truly measure the forecasting ability of the model.

In measuring forecast errors,the MAD and the square root of the MSE will provide similar (but not identical)values,in that both provide a measure of the "typical" amount of error in forecasts.

A plot of the time series with time on the horizontal axis is an effective means of assessing whether the series is linear or nonlinear.

The Baker's Candy Company has been in business for three years.The quarterly sales data for the company are shown as follows: As a first step in computing a seasonal index,the four-period moving average corresponding to the mid-point between periods 2 and 3 is 3,350.

Forecast bias measures the average amount of error per forecast,so a positive value means that forecasts tended to be too low.

In comparing two or more forecasting models,the MAD value is useful in determining how successful the models were in fitting historical data.

It is possible to use linear regression analysis to develop a forecasting model for nonlinear data if we can effectively transform the data.

A seasonal index is a statistic that is computed from time-series data to indicate the effect of the seasonality in the time-series data.

The reason for using split samples in developing a forecasting model is to eliminate the potential for bias in the resulting model.

The Baker's Candy Company has been in business for three years.The quarterly sales data for the company are shown as follows: Based on this information,the data reflect both a linear trend and seasonal components.

From an annual time series of a company's sales the linear trend model Ft = 127 + 54(t)has been developed.This means that on average sales have been increasing by 127 per year.

You are given the following linear trend model: F_t = 345.60 - 200.5(t).This model implies that in year 1,the dependent variable had a value of 145.1.

From an annual time series of a company's sales the linear trend model F_t = 127 + 54(t)has been developed.This means that on average sales have been increasing by 127 per year.