Math Problem Statement
Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is
Estimated College GPA=2.96+0.093(High School GPA).
GPAs College GPA High School GPA 3.79 2.56 3.15 4.00 3.10 4.39 3.68 4.93 3.65 4.84 2.61 3.21 Step 3 of 3 : Compute the standard error (se ) of the model. Round your answer to four decimal places.
Solution
To compute the standard error of the regression model (se), we follow these steps:
Step 1: Compute the Residual Sum of Squares (SSE)
The standard error of the regression is given by:
where:
- is the sum of squared errors (also called the residual sum of squares).
- is the number of observations.
- The errors (residuals) are the differences between the actual College GPA and the predicted College GPA.
Step 2: Compute Predicted College GPAs
Using the regression equation:
where is the High School GPA, and is the predicted College GPA.
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Math Problem Analysis
Mathematical Concepts
Regression Analysis
Standard Error
Residual Sum of Squares
Formulas
Estimated College GPA = 2.96 + 0.093(High School GPA)
Standard Error, se = sqrt(SSE / (n - 2))
Theorems
Least Squares Regression
Suitable Grade Level
Grades 11-12
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