Standard Error of Estimate Explained | Simplified Explanation| @perfectcommercecoaching

The Standard Error of Estimate (SEE) is a statistical term that measures the accuracy of predictions made by a regression model. It quantifies the average distance that the observed values fall from the regression line. Essentially, it reflects how well the model fits the data.

Calculation of Standard Error of Estimate
Fit a Regression Model: First, you fit a regression model to your data, which involves estimating the coefficients (parameters).

Calculate Predicted Values: Use the regression equation to calculate the predicted values (
𝑌
′
Y
′
) for each observation in your dataset.

Calculate Residuals: Determine the residuals (the differences between the observed values
𝑌
Y and the predicted values
𝑌
′
Y
′
):

Residual
=
𝑌
−
𝑌
′
Residual=Y−Y
′

Square the Residuals: Square each of the residuals:

Squared Residual
=
(
𝑌
−
𝑌
′
)
2
Squared Residual=(Y−Y
′
)
2

Calculate Mean of Squared Residuals: Compute the mean of the squared residuals:

Mean Squared Error (MSE)
=
∑
(
𝑌
−
𝑌
′
)
2
𝑛
−
𝑝
Mean Squared Error (MSE)=
n−p
∑(Y−Y
′
)
2

​

𝑛
n is the total number of observations.
𝑝
p is the number of parameters in the model (including the intercept).
Standard Error of Estimate: Finally, take the square root of the MSE to obtain the Standard Error of Estimate:

SEE
=
MSE
=
∑
(
𝑌
−
𝑌
′
)
2
𝑛
−
𝑝
SEE=
MSE
​
=
n−p
∑(Y−Y
′
)
2

​

​

Interpretation
A smaller SEE indicates a better fit of the model to the data, meaning the predicted values are closer to the actual values.
A larger SEE suggests that the predictions are more spread out from the actual values, indicating a poorer fit.
Applications
It is commonly used in regression analysis to evaluate the performance of a model.
It helps in comparing the predictive accuracy of different models.
If you need more specific examples or applications, feel free to ask!

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