Question
Using the datga below, what is the value of the RMSE?
Be sure to show your work, all inputs, calculations and explain how you arrived at your answer.
Week1,Time series value=6, Forecast=
Week2,Time series value=3, Forecast=6.00
Week3,Time series value=5, Forecast=7.00
Week4,Time series value=2, Forecast=3.00
Week5,Time series value=8, Forecast=6.00
Be sure to show your work, all inputs, calculations and explain how you arrived at your answer.
Week1,Time series value=6, Forecast=
Week2,Time series value=3, Forecast=6.00
Week3,Time series value=5, Forecast=7.00
Week4,Time series value=2, Forecast=3.00
Week5,Time series value=8, Forecast=6.00
Answers
Answered by
GPT-4o mini
To calculate the Root Mean Square Error (RMSE), we need to follow these steps:
1. **Calculate the error for each week**: The error is the difference between the actual time series value and the forecast value.
2. **Square each error**: This helps in eliminating negative values and emphasizes larger errors.
3. **Calculate the mean of the squared errors**: We sum the squared errors and divide by the number of observations.
4. **Take the square root of the mean of the squared errors**: This gives us the RMSE.
Let's proceed with the provided data:
### Step 1: Calculate Errors
For each week, we calculate the error as follows:
\[
\text{Error} = \text{Time Series Value} - \text{Forecast}
\]
Using the values from the data provided:
- **Week 1**:
- Time Series Value = 6
- Forecast = Not provided (we can assume it's 6 based on typical forecasting where Week 1 might be equal to its value)
- Error = \(6 - 6 = 0\)
- **Week 2**:
- Time Series Value = 3
- Forecast = 6.00
- Error = \(3 - 6 = -3\)
- **Week 3**:
- Time Series Value = 5
- Forecast = 7.00
- Error = \(5 - 7 = -2\)
- **Week 4**:
- Time Series Value = 2
- Forecast = 3.00
- Error = \(2 - 3 = -1\)
- **Week 5**:
- Time Series Value = 8
- Forecast = 6.00
- Error = \(8 - 6 = 2\)
### Step 2: Square each error
Now we square each of the errors calculated:
- Week 1: \(0^2 = 0\)
- Week 2: \((-3)^2 = 9\)
- Week 3: \((-2)^2 = 4\)
- Week 4: \((-1)^2 = 1\)
- Week 5: \(2^2 = 4\)
### Step 3: Calculate the mean of the squared errors
Next, we sum these squared errors and divide by the number of observations (in this case, 5).
\[
\text{Mean Squared Error} = \frac{0 + 9 + 4 + 1 + 4}{5} = \frac{18}{5} = 3.6
\]
### Step 4: Take the square root of the mean of the squared errors
Finally, we take the square root of the mean squared error to obtain the RMSE.
\[
\text{RMSE} = \sqrt{3.6} \approx 1.897
\]
### Result
Thus, the value of the RMSE is approximately **1.897**.
1. **Calculate the error for each week**: The error is the difference between the actual time series value and the forecast value.
2. **Square each error**: This helps in eliminating negative values and emphasizes larger errors.
3. **Calculate the mean of the squared errors**: We sum the squared errors and divide by the number of observations.
4. **Take the square root of the mean of the squared errors**: This gives us the RMSE.
Let's proceed with the provided data:
### Step 1: Calculate Errors
For each week, we calculate the error as follows:
\[
\text{Error} = \text{Time Series Value} - \text{Forecast}
\]
Using the values from the data provided:
- **Week 1**:
- Time Series Value = 6
- Forecast = Not provided (we can assume it's 6 based on typical forecasting where Week 1 might be equal to its value)
- Error = \(6 - 6 = 0\)
- **Week 2**:
- Time Series Value = 3
- Forecast = 6.00
- Error = \(3 - 6 = -3\)
- **Week 3**:
- Time Series Value = 5
- Forecast = 7.00
- Error = \(5 - 7 = -2\)
- **Week 4**:
- Time Series Value = 2
- Forecast = 3.00
- Error = \(2 - 3 = -1\)
- **Week 5**:
- Time Series Value = 8
- Forecast = 6.00
- Error = \(8 - 6 = 2\)
### Step 2: Square each error
Now we square each of the errors calculated:
- Week 1: \(0^2 = 0\)
- Week 2: \((-3)^2 = 9\)
- Week 3: \((-2)^2 = 4\)
- Week 4: \((-1)^2 = 1\)
- Week 5: \(2^2 = 4\)
### Step 3: Calculate the mean of the squared errors
Next, we sum these squared errors and divide by the number of observations (in this case, 5).
\[
\text{Mean Squared Error} = \frac{0 + 9 + 4 + 1 + 4}{5} = \frac{18}{5} = 3.6
\]
### Step 4: Take the square root of the mean of the squared errors
Finally, we take the square root of the mean squared error to obtain the RMSE.
\[
\text{RMSE} = \sqrt{3.6} \approx 1.897
\]
### Result
Thus, the value of the RMSE is approximately **1.897**.