AN 300 Final Exam
Adjusted Coefficient of Determination, adjusted R^2
- RSquare Adj.- R^2 increases with more independent variables- Adjusted R^2 imposes a penalty for any additional independent variable- Negative Adjusted R^2 means the additional independent variable does not help with predicting the dependent variable- Use Adjusted R^2 to compare models with different number of independent variables- The higher the adjusted R^2, the better the model- Adjusted R^2 < R^2
Standard error of the estimate, Se
- Root mean squared error- Standard deviation of the residue (i.e., the difference between the observed and the predicted values of the dependent variable)- 0 <= Se < infinity- Se = 0 means the residue is zero- The closer Se is to zero, the better the model fit
Coefficient of Determination, R^2
- Rsquare- The proportion of the sample variation in the dependent variable that is explained by the estimated regression equation- 0 <= R^2 <= 1- R^2 = 1 means all the observed and predicted values of the dependent variable in the sample are identical- The closer R^2 is to one, the better the fit
The actual demand and forecast demand for January is 5 and 37 respectively. What is its forecast error?
-32
Which of the following is TRUE about linear regression? Check all that apply. -It answers what could happen questions. -The higher the goodness of fit measure, the better the regression model fit. -It is used by marketers to predict sales based on advertising expenditure on multiple communication channels. -When you have more independent variables in the regression model, the value of both RSquare and RSquare Adj will increase. -Adjusted coefficient of determination can be negative.
-It answers what could happen questions. -It is used by marketers to predict sales based on advertising expenditure on multiple communication channels. -Adjusted coefficient of determination can be negative.
Which of the following is true about the estimating regression process? Check all that apply. -It estimates the intercept and slope of the regression equation. -It uses partial least square method. -It minimizes the sum of the squared differences between the observed and predicted values of the dependent variable. -There is a random error term in the estimated equation. -It estimates only the slope of the regression equation.
-It estimates the intercept and slope of the regression equation. -It minimizes the sum of the squared differences between the observed and predicted values of the dependent variable.
Which of the following statements about time-series forecasting is TRUE? Check all that apply. -It only works with trend data patterns. -It is a predictive analytics method. -It is a predictive analytics technique. -It applies to strategic planning by predicting market growth rate. -It needs data on observations of an item of interest over time. -It answers what should happen questions. -It predicts the future outcome of the item of interest.
-It is a predictive analytics technique. -It applies to strategic planning by predicting market growth rate. -It needs data on observations of an item of interest over time. -It predicts the future outcome of the item of interest.
Which of the following statements about MAPE is TRUE? Check all that apply. -It is unitless. -It can be negative. -It can be used to compare two applications of the same forecasting method. -It can tell whether or not the method is biased. -It stands for Mean Average Percentage Error. -It has no error cancellation problem.
-It is unitless. -It can be used to compare two applications of the same forecasting method. -It has no error cancellation problem.
Which of the following statements about time-series forecasting methods is TRUE? Check all that apply. -Linear Regression is the method of choice for data with a trend pattern. -You choose a large value for alpha when using the Exponential Smoothing method to give less weight to the most recent data. -Linear Regression for Seasonality without Trend method is appropriate for data with a seasonal pattern only. -There is no time-series forecasting method for data with both seasonal and trend patterns. -You choose a small value for "k" when using the Simple Moving Average method of order "k" to track movement in the most recent data. -Linear Regression uses the time period as the dependent variable. -The Simple Average method is also known as the Historical Moving Average method.
-Linear Regression is the method of choice for data with a trend pattern. -Linear Regression for Seasonality without Trend method is appropriate for data with a seasonal pattern only. -You choose a small value for "k" when using the Simple Moving Average method of order "k" to track movement in the most recent data. -The Simple Average method is also known as the Historical Moving Average method.
Which of the following statements about linear regression is TRUE? Check all that apply. -It answers what should happen questions. -Multiple regression has two or more independent variables. -It is a predictive analytics technique. -The relationship between the outcome and input variables is linear. -The variable of interest being predicted is called an independent variable. -It has only one dependent variable.
-Multiple regression has two or more independent variables. -It is a predictive analytics technique. -The relationship between the outcome and input variables is linear. -It has only one dependent variable.
Which of the following time-series forecasting smoothing methods is selected as least biased in this application to track the recent movement of data to forecast COVID mortality? -Simple average -Exponential smoothing with alpha = 0.9 -Naive -Linear regression -Moving average with k=3
-Naive
Which of the following is performed to modify the data from the Data Visualization Application for time series forecasting in this application? Check all that apply. -Change the data type of the Month column from numeric to categorical. -Remove columns that are irrelevant. -Add indicator columns for seasonality. -Add a column to aggregate the number of COVID deaths by month. -Add a column to account for the time period in the series.
-Remove columns that are irrelevant. -Add indicator columns for seasonality.
Which of the following statements about MAE and SSE is FALSE? Check all that apply. -SSE is the scaled down version of MAE. - They can be used to compare two applications of the same forecasting method. -SSE stands for Sum of Standard Errors. -MAE is always greater than SSE. -They are unitless. -Lower values are preferred. -Errors do not cancel out each other. -None can be negative. -MAE stands for Mean Absolute Error. -A positive value means the forecasting method is biased.
-SSE is the scaled down version of MAE. - They can be used to compare two applications of the same forecasting method. -SSE stands for Sum of Standard Errors. -MAE is always greater than SSE. -They are unitless. -A positive value means the forecasting method is biased.
Which of the following is a business application of time series forecasting? -Sales forecast of swimsuits from advertising expenditure. -Sales forecast of swimsuits from a survey of vacationers. -Sales forecasts of swimsuits from past records. -Sales forecast of swimsuits from demand of sunglasses.
-Sales forecasts of swimsuits from past records.
Which of the following methods is used to estimate the values of the independent variables for next month in this application to make a prediction of monthly COVID deaths? -Simple regression -Exponential smoothing -Naive -Multiple regression -Simple average
-Simple average
Which of the following time-series forecasting smoothing methods is selected as most accurate in this application to track the recent movement of data to forecast COVID mortality? -Naive -Linear regression -Simple average -Moving average with k=3 -Exponential smoothing with alpha = 0.9
-Simple average
Which of the following is not a goodness of fit measure for linear regression? -Standard error of the estimate -Coefficient of determination -Adjusted coefficient of determination -Standard coefficient
-Standard coefficient
Which of the following is a data requirement for linear regression. Check all that apply. -The dependent variable must be categorical in value. -There are multiple columns of dependent variables. -The dependent variable must be numerical in value. -The variables must be organized in a table with each variable as a row. -The independent variables must be numerical in value.
-The dependent variable must be numerical in value. -The independent variables must be numerical in value.
The relevant information from the regression report includes _________. Check all that apply. -The predicted value. -The regression equation. -The goodness-of-fit measures. -The slope coefficients for the independent variables. -The slope coefficients for the dependent variable.
-The regression equation. -The goodness-of-fit measures. -The slope coefficients for the independent variables.
Which of the following statements about CFE and MFE is FALSE? Check all that apply. -MFE stands for Mean Forecast Error. -The biases are aggregated. -CFE stands for Cumulative Forecast Error. -They are unitless. -Positive errors may be offset by the -negative ones. -CFE is the scaled down version of MFE. -A positive CFE means the forecasting method is biased towards overestimating. -The least biased CFE/MFE is preferred. -They cannot be negative.
-They are unitless. -CFE is the scaled down version of MFE. -A positive CFE means the forecasting method is biased towards overestimating. -They cannot be negative.
You want to capture the seasonal variations of spring, summer, fall, and winter on sales of swimsuits using a regression model. Which of the following statements is TRUE? Check all that apply. -Three dummy variables should be used in the model. -A simple regression model should be used. -Four dummy variables should be used in the model. -A multiple regression model should be used.
-Three dummy variables should be used in the model. -A multiple regression model should be used.
Which of the following is NOT one of the forecast error metrics that you learned in this class? -Sum of Squared Errors -Mean Absolute Percentage Error -Mean Forecast Error -Tracking signal -Cumulative Forecast Error
-Tracking signal
Which of the following is a data pattern in time-series data that can be uncovered by time-series forecasting? Check all that apply. -Trend -Level -Random -Horizontal -Cycle -Vertical
-Trend -Level -Horizontal -Cycle
What kind of data pattern is depicted in the following line graph? Check all that apply. Its a graph with a straight red line angled positively. There is a Blue line that begins below the red line and then had alternating periods above and below the line. -Trend -Random -Level -Seasonality -Cycle
-Trend -Seasonality
Which of the following is FALSE about time-series forecasting? Check all that apply. -it uncovers natural groupings of objects. -It uses a line graph to visualize trends in data. -It uses historical values of data on an item of interest. -It discovers random errors in data. -It is a prescriptive analytics technique. -It generates product demand forecasts for market basket analysis. -It answers what could happen questions.
-it uncovers natural groupings of objects. -It discovers random errors in data. -It is a prescriptive analytics technique. -It generates product demand forecasts for market basket analysis.
The actual demand and forecast demand for January is 3 and 3 respectively. What is its forecast error?
0
Given the following sales data (in $000) for C&A's product: January -15 February -18 March -14 April -16 May -13 June -16 1. What is the naive forecast for June? 2. What is the historical moving average forecast for July? (rounded to 2 decimal places) 3. What is the simple moving average forecast of order 3 for June? (rounded to 2 decimal places) 4. What is the simple moving average forecast of order 1 for June? 5. What is the exponential smoothing forecast for July if alpha = 0.2 and the forecast for February is 15? (rounded to 2 decimal places) 6. The simple moving average method of order 1 is the same as the Naive method. (T/F)
1. 13 (Apply May to June) 2. 15.33 (All months sales/number of months) 3. 14.33 ((14+16+13)/3) 4. 13 (may one back) 5. 15.15 (Forecast for March = .2*Actual Feb + (1-.2)*Forecast Feb ... this continues through the months until reaching July) Forecast April (.2*14 + .8*march forecast)... 6. T
Regression Process
1. Modeling - use an equation to describe the relationship between the dependent and independent variables2. Estimating - use the ordinary least squares method to produce the regression equation that is "closest" to the data3. Evaluating - examine several "goodness-of-fit" measures to select the regression equation that fits the data best
Given the following actual and forecast data: January -Actual 1250 , Forecast 1050 February -Actual 1200 , Forecast 1133.33 March -Actual 1280 , Forecast 1183.33 April -Actual 1300 , Forecast 1243.33 May -Actual 1350 , Forecast 1260 June -Actual 1300 , Forecast 1310 What is the forecast error for June? :-90 :-10 :10 :90
: -10
Given the following actual and forecast data: January -Actual 1250 , Forecast 1050 February -Actual 1200 , Forecast 1133.33 March -Actual 1280 , Forecast 1183.33 April -Actual 1300 , Forecast 1243.33 May -Actual 1350 , Forecast 1260 June -Actual 1300 , Forecast 1310 What is the absolute error for June? : 90 : 10 : -10 : -90
: 10
Match the kind of time series forecasts to be generated on the left with the most appropriate linear regression model on the right. Time series forecasts for seasonality.
A multiple regression model with indicator variables as the independent variables
Time series forecasts for seasonality with trend.
A multiple regression with indicator variables and time period as the independent variables.
Time series forecasts for trend.
A simple regression model with time period as the independent variable.
Given the following actual and forecast sales data for C&A's chocolate: Month / Sales ($ Million) / Forecast Jan / 42.74 / - Feb / 40.24 / 42.74 Mar / 35.85 / 40.74 Apr / 43.37 / 36.80 May / 42.45 / 42.06 A. What is the Forecast Error for February, March and April? B. What is the Mean Forecast Error (MFE) for April? C. What is the Absolute Percentage Error (APE) for February and March? D. What is the Mean Absolute Percentage Error (MAPE) for March? E. The forecast for March is negatively biased (T/F). F. The forecast over-estimates the actual in April (T/F). G. An APE of100 means that its forecast and actual values are the same (T/F). H. MAPE can be negative (T/F).
A. FE_Feb = 40.24 - 42.74 = 2.5; FE_Mar = 35.85 - 40.74 = -4.92; FE_April = 43.37 - 36.80 = 6.57 B. -2.5 - 4.92 + 6.57 / 3 = -0.28 C. APE_Feb = |40.24-42.74|/ 40.24 * 100 = 6.21; APE_Mar = |35.85-40.74|/35.85*100 = 13.74 D. 6.21+13.74/2 = 9.97 E. T - forecast error is negative which means it is negatively biased. F. F - forecast is less than actual which means it under-estimates the actual G. F - APE is 100 means the absolute error has the same value as the actual. H. F - absolute error cannot be negative which means APE/MAPE cannot be negative
Which of the following statements concerning Linear Regression is TRUE? Check all that apply. A. Linear Regression can have more than one independent variable. B. Multiple Regression must have two or more dependent variables. C. The estimating process of linear regression is about describing the relationship between the outcome and input variables. D. The predicted value of the outcome can be equal to the intercept of a linear regression equation. E. We can use ordinary least squares to evaluate the goodness of fit of a linear regression model. F. The value of Coefficient of Determination can be 100. G. Adjusted Coefficient of Determination should be used to evaluate the goodness of fit of multiple regression models. H. The method that has the highest value of Root Mean Squared Error is the one with the best fit.
A. T - multiple regression has two or more independent variables, linear regression is one. B. F - linear regression has only one dependent variable. C. F - the estimating process is about determining the slope and intercept of the regression equation. D. T - if all independent variables are zero. E. F - OLS is the method used in the estimating process for linear regression. F. F - o<= R^2 <= 1 G. T - it informs the value of additional independent variables in the model H. F - 0 <= RMSE < = infinity, therefore, the closer RMSE to zero (or the lowest value) the better.
Given the following sales data for C&A's chocolate: Month Sales ($ Million) Jan 42.74 Feb 40.24 Mar 35.85 Apr 43.37 May 42.25 A. What kind of data pattern is observed in the given sales data? B. What is the Simple Average forecast for May? C. What is the Exponential Smoothing forecast for April if α= 0.8 and the forecast for February is the actual of January, i.e., 42.74? D. Naïve method requires the least amount of historical data to perform forecasting (T/F). E. For Simple Moving Average method, an order (i.e., k) of four yields the same forecasted value for May as the Simple Average method (T/F). F. For Exponential Smoothing method, an αclose to zero should be used to give more weight to recent data (T/F). G. Linear Regression with trend adapts well to sudden shift in data pattern (T/F).
A. level B. 42.74+40.24+35.85+43.37/4 = 40.54 C. Forecast for March = (0.8*40.24+0.2*42.74 = 40.74); (Forecast for April = 0.8*35.85_0.2*40.74 = 36.80 D. T -only need one data point E. T - 40.54 is the may forecast F. F 0< a < 1, a value close to zero means less weight is given to the most recent data. G. F - it works well for trend data pattern
It divides the absolute error of a period by the actual value of that period. The resulting quotient is then multiplied by 100.
Absolute percentage error
It should be used to compare models with different numbers of independent variables.
Adjusted coefficient of determination
Its value can be negative.
Adjusted coefficient of determination
You selected time series forecasting for seasonality. as the best-fit model to capture the trend and/or seasonal data patterns in this application because its RSquare Adj is highest .
Answer 1: time series forecasting for seasonality. Answer 2: RSquare Adj Answer 3: higest
The best-fit model selected in this application should be the one with the [ Select ] ["lowest", "zero", "highest", "postive", "negative"] value of [ Select ] ["RSquare", "Cumulative forecast error", "Adjusted error of the estimate", "RSquare Adj", "Mean absolute error"] .
Answer 1: highest Answer 2: RSquare Adj
The closer its value to one, the better the model fit.
Coefficient of determination
The proportion of the sample variation in the dependent variable that is explained by the estimated regression equation.
Coefficient of determination
Match the definition on the left with the forecasting error metric to which it applies on the right. It sums up all the errors available.
Cumulative Forecast error
It is the variable of interest being predicted.
Dependent variable
A gradual decrease in values over time.
Downward Trend
Use the ordinary least squares method to produce an equation that is closest to the data.
Estimating
Examine several goodness of fit measures to select the best equation.
Evaluating
It is a weighted average of all prior historical actual vales.
Exponential smoothing average
A large number of time periods should be used as k in simple moving average forecast of order k in order to track movement in the most recent data points.
F
A linear trend line cannot have a zero intercept.
F
Four dummy variables should be used in the linear trend line equation to represent the effect of each of the four seasons on the forecast.
F
Linear regression adapts to sudden shifts to data patterns.
F
Smoothing method is appropriate for data with a trend pattern.
F
Evaluating
Goodness of fit measures:- Standard error of the estimate, Se- Coefficient of determination, R^2- Adjusted coefficient of determination, adjusted R^2
A constant average value over time.
Level
It uses the "best fit" linear trend line to make predictions.
Linear Regression
It uses indicator variables to capture variations.
Linear regression for seasonality
It averages all the errors available.
Mean Absolute error
You want to compare two different applications of the same forecasting method.
Mean absolute error percentage
It takes the average of the absolute percentage error values over a range of time periods.
Mean absolute percentage error
Match the situation on the left with the appropriate forecast error metrics on the right. You want to know if the forecast method is biased or not.
Mean forecast error
You have a negative forecast error.
Mean forecast error
Use a dummy variable to describe a categorical independent variable.
Modeling
It adapts readily to sudden shifts in data pattern.
Naive
Match the characteristics on the left with the most appropriate forecasting methods to which it applies on the right. It requires only one historical data value.
Naive
It is used to minimize the error sum of squares to determine the parameters of the regression equation.
Ordinary least squares method
It uses an equation to capture the relationship between variables.
Regression Modeling
A recurring pattern that occurs at set periods within a larger time frame.
Seasonality
It is used to predict the outcome of a variable of interest based on the value of one variable.
Simple Regression
It requires the data points in the time series as well as the number of periods used in forecasting.
Simple moving average
Match the description on the left with the appropriate goodness of fit measure on the right. It is the standard deviation of the residue.
Standard error of the estimate
The closer its value to zero, the better the model fit.
Standard error of the estimate
It sums up all the squared error available.
Sum of squared error
You want to emphasize large errors.
Sum of squared errors
A linear trend line with a positive slope indicates a gradual upward shift in data values.
T
Historical moving average method is also known as simple average method.
T
Indicate whether the following statements are T/F. A high value of alpha places more weight to recent data in generating the next period's exponential smoothing forecast.
T
Naive method needs only one historical data point to be given.
T
Time period is an independent variable in a linear regression with trend model.
T
A gradual increase in values over time.
Upward Trend
Estimating
Use sample data to estimate the intercept and slope(s) of the regression equation with the ordinary least squares (OLS) methodThe OLS method minimizes the error sum of squares (SSE) in estimating the intercept and slope(s) of the regression lineSSE is the sum of squared differences between the observed and predicted values of the dependent variable- Estimated simple regression equation: y = a + b x- Estimated multiple regression equation: y = a + b1 x1 + b2 x2 + ... + bn xn
Match the description on the left with the regression process it illustrates on the right. Use an equation to describe the relationship between dependent and independent variable(s).
modeling
It is used to predict the outcome of a variable of interest based on the value of a categorical variable.
multiple regression