Questions: Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is Estimated College GPA = 4.28 + (- 0.2134)(High School GPA) Compute the sum of squared errors (SSE) for the model. Round your answer to four decimal places. GPAs College GPA High School GPA 3.86 3.15 3.95 2.27 2.86 4.02 3.42 3.08 3.94 2.71 3.00 4.51

Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is

Estimated College GPA = 4.28 + (- 0.2134)(High School GPA)

Compute the sum of squared errors (SSE) for the model. Round your answer to four decimal places.

GPAs
College GPA  High School GPA
3.86  3.15
3.95  2.27
2.86  4.02
3.42  3.08
3.94  2.71
3.00  4.51
Transcript text: Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is Estimated College GPA = 4.28 + (- 0.2134)(High School GPA) Compute the sum of squared errors (SSE) for the model. Round your answer to four decimal places. GPAs College GPA | High School GPA 3.86 | 3.15 3.95 | 2.27 2.86 | 4.02 3.42 | 3.08 3.94 | 2.71 3.00 | 4.51
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Solution

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Solution Steps

Step 1: Calculate Predicted College GPA

Using the given regression equation:

Estimated College GPA=4.28+(0.2134)×High School GPA \text{Estimated College GPA} = 4.28 + (-0.2134) \times \text{High School GPA}

We calculate the predicted College GPA for each High School GPA:

  • For High School GPA = 3.15: Predicted College GPA=4.28+(0.2134)×3.15=3.6078 \text{Predicted College GPA} = 4.28 + (-0.2134) \times 3.15 = 3.6078

  • For High School GPA = 2.27: Predicted College GPA=4.28+(0.2134)×2.27=3.7956 \text{Predicted College GPA} = 4.28 + (-0.2134) \times 2.27 = 3.7956

  • For High School GPA = 4.02: Predicted College GPA=4.28+(0.2134)×4.02=3.4221 \text{Predicted College GPA} = 4.28 + (-0.2134) \times 4.02 = 3.4221

  • For High School GPA = 3.08: Predicted College GPA=4.28+(0.2134)×3.08=3.6227 \text{Predicted College GPA} = 4.28 + (-0.2134) \times 3.08 = 3.6227

  • For High School GPA = 2.71: Predicted College GPA=4.28+(0.2134)×2.71=3.7017 \text{Predicted College GPA} = 4.28 + (-0.2134) \times 2.71 = 3.7017

  • For High School GPA = 4.51: Predicted College GPA=4.28+(0.2134)×4.51=3.3176 \text{Predicted College GPA} = 4.28 + (-0.2134) \times 4.51 = 3.3176

Step 2: Calculate Sum of Squared Errors (SSE)

The Sum of Squared Errors (SSE) is calculated using the formula:

SSE=(Actual College GPAPredicted College GPA)2 \text{SSE} = \sum (\text{Actual College GPA} - \text{Predicted College GPA})^2

Substituting the actual and predicted values:

SSE=(3.863.6078)2+(3.953.7956)2+(2.863.4221)2+(3.423.6227)2+(3.943.7017)2+(3.003.3176)2 \text{SSE} = (3.86 - 3.6078)^2 + (3.95 - 3.7956)^2 + (2.86 - 3.4221)^2 + (3.42 - 3.6227)^2 + (3.94 - 3.7017)^2 + (3.00 - 3.3176)^2

Calculating each term:

=0.0635+0.0238+0.3168+0.0411+0.0568+0.1002 = 0.0635 + 0.0238 + 0.3168 + 0.0411 + 0.0568 + 0.1002

Summing these values gives:

SSE=0.6022 \text{SSE} = 0.6022

Final Answer

The sum of squared errors (SSE) for the model is:

0.6022 \boxed{0.6022}

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