Question

The residuals for a data set are:

0.05, 0.30, -0.42, 0.61, -0.89, 0.74, 0.46
To 2 decimal places, what is the root mean square error?

Answer 1

The root mean square error (RMSE) for the given data set of residuals is calculated by squaring each of the residuals, summing them up, dividing by the number of residuals to find the mean square, and then taking the square root of the mean square. The RMSE is approximately 0.56 to two decimal places.

Step-by-step explanation:

Calculating Root Mean Square Error (RMSE)

To calculate the root mean square error (RMSE) for the given data set, follow the steps below:

1. Square each residual value to remove any negative signs and to give greater weight to larger errors.
2. Sum all the squared residuals to get the total sum of squares (SS).
3. Divide the SS by the number of residuals to find the mean square.
4. Take the square root of the mean square to get the RMSE.

Let's apply these steps to the given residuals:

1. Squared residuals: (0.05)^2, (0.30)^2, (-0.42)^2, (0.61)^2, (-0.89)^2, (0.74)^2, (0.46)^2
2. SS = 0.0025 + 0.09 + 0.1764 + 0.3721 + 0.7921 + 0.5476 + 0.2116 = 2.1923
3. Mean square = 2.1923 / 7 = 0.31319
4. RMSE = √0.31319 ≈ 0.56 (to two decimal places)

Therefore, the RMSE for this data set is 0.56 to two decimal places.