You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation: y = 12.06 + 0.12x Calculate the value of SSE; round your answer to three decimal places.
The Correct Answer and Explanation is:
To calculate the value of the Sum of Squared Errors (SSE), we need more information than just the equation of the regression line. Specifically, we need the observed values of y and the corresponding predicted values of y based on the regression equation. However, I will outline the process for calculating the SSE using the regression equation.
The regression equation is:
y=12.06+0.12xy = 12.06 + 0.12xy=12.06+0.12x
Steps to Calculate SSE:
- Obtain the Observed Values of y:
- These are the actual values of the dependent variable y that you have collected in your dataset.
- Calculate the Predicted Values of y (ŷ):
- For each value of x, substitute it into the regression equation to calculate the predicted value of y (denoted as ŷ).
If x = 5, then:
y^=12.06+0.12(5)=12.06+0.60=12.66ŷ = 12.06 + 0.12(5) = 12.06 + 0.60 = 12.66y^=12.06+0.12(5)=12.06+0.60=12.66 - Calculate the Errors (Residuals):
- The error (or residual) for each observation is the difference between the observed value y and the predicted value ŷ.
If the observed value is y = 14, and the predicted value ŷ = 12.66, then:
e=14−12.66=1.34e = 14 – 12.66 = 1.34e=14−12.66=1.34 - Square the Errors:
- For each observation, square the error (residual).
- Sum the Squared Errors:
- Sum all the squared errors to obtain the Sum of Squared Errors (SSE).
Formula Recap:
SSE=∑(y−(12.06+0.12x))2SSE = \sum (y – (12.06 + 0.12x))^2SSE=∑(y−(12.06+0.12x))2
Once you have all the values of y and x, you can compute SSE by following the outlined steps.
