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
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
Solution
Solution Steps
Step 1: Calculate Predicted College GPA
Using the given regression equation:
Estimated College GPA=4.28+(−0.2134)×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
For High School GPA = 2.27:
Predicted College GPA=4.28+(−0.2134)×2.27=3.7956
For High School GPA = 4.02:
Predicted College GPA=4.28+(−0.2134)×4.02=3.4221
For High School GPA = 3.08:
Predicted College GPA=4.28+(−0.2134)×3.08=3.6227
For High School GPA = 2.71:
Predicted College GPA=4.28+(−0.2134)×2.71=3.7017
For High School GPA = 4.51:
Predicted College GPA=4.28+(−0.2134)×4.51=3.3176
Step 2: Calculate Sum of Squared Errors (SSE)
The Sum of Squared Errors (SSE) is calculated using the formula: