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:

se=SSEn2s_e = \sqrt{\frac{SSE}{n - 2}}

where:

  • SSESSE is the sum of squared errors (also called the residual sum of squares).
  • nn 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:

Y^=2.96+0.093(X)\hat{Y} = 2.96 + 0.093(X)

where XX is the High School GPA, and Y^\hat{Y} 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