CH 4 EXAMPLES_ UPDATE_ 2024

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Economics

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Feb 20, 2024

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FORECASTING excel: For Trend and Regression Questions: Models: = INTERCEPT(knownYs, knownXs) Naïve = SLOPE(knownYs, knownXs) Moving Average Weighted Moving Average Exponential Smoothing a (alpha) F(t+1) =alpha*At + (1-a)*Ft Trend y = a + b(x) - x equals time Regression Analysis y = a + b(x) - x equals something other than y = a + b(x1)…b(x2)…b(x3) Error Analysis MAD (mean absolute deviation) difference between forecast & actual MSE (mean squared error) MAD^2 MAPE (mean absolute percent error) MAD/Actual coefficient correlation r how strong is the relationship between x and y coefficient of determination r^2 how much can be determined from the regression line
n time excel: =correl(knownYs, knownXs) e r^2
Forecasting MAD Actual Demand At 3 mo. Moving Average Forecast 4.53 Sales of industrial vacuum cleaners at Larry Armstrong Supply Co. over the past 13 months are shown below: Month Jan. Feb. March April May June July Sales (in thousands) 11 14 16 10 15 17 11 Month Aug. Sept. Oct. Nov. Dec. Jan. Sales (in thousands) 14 17 12 14 16 11 a) Using a moving average with 3 periods, determine the demand for vacuum cleaners for next February. b) Using a weighted moving average with 3 periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would have a weight of 2, and January would have a weight of 3. c) Using MAD, determine which is the better forecast.
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Forecasting MAD Actual Demand At 3 mo. Weighted Moving Average (1,2,3) Forecast 4.53 Sales of industrial vacuum cleaners at Larry Armstrong Supply Co. over the past 13 months are shown below: Month Jan. Feb. March April May June July Sales (in thousands) 11 14 16 10 15 17 11 Month Aug. Sept. Oct. Nov. Dec. Jan. Sales (in thousands) 14 17 12 14 16 11 a) Using a moving average with 3 periods, determine the demand for vacuum cleaners for next February. b) Using a weighted moving average with 3 periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would have a weight of 2, and January would have a weight of 3. c) Using MAD, determine which is the better forecast.
ALPHA TIME DEMAND (At) FORECAST (Ft) MAD 4.54 Passenger miles flown on Northeast Airlines, a commuter firm serving the Boston hub, are shown for the past 12 weeks: Week 1 2 3 4 5 6 7 8 9 10 11 12 Actual Passenger Miles (in thousands) 17 21 19 23 18 16 20 18 22 20 15 22 a) Assuming an initial forecast for week 1 of 17,000 miles, use exponential smoothing to compute miles for weeks 2 through 12. Use α = .2. b) What is the MAD for this model? Compute the Cumulative Forecast Errors
Exponential Smoothing Formula: F(t+1) =alpha*At + (1-a)*Ft
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y = a + b(x) excel - trend line: Time MAD x y intercept slope Correlation Coefficient Coefficient Determination Overall MAD Actual Demand Dt Trend FORECAS T 4.55 Given the following data, use least squares regression to derive a trend equation. What is your estimate of the demand in period 7? In period 12? Period 1 2 3 4 5 6 Demand 7 9 5 11 10 13
y = a + b(x) X Variable Forecast MAD Intercept Slope Correlation Coefficient Coefficient Determination Overall MAD Actual Demand Y
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