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

Solution Steps

Using the given regression equation:

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

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

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

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

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

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

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

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

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

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

Substituting the actual and predicted values:

\[ \text{SSE} = (3.86 - 3.6078)^2 + (3.95 - 3.7956)^2 + (2.86 - 3.4221)^2 + (3.42 - 3.6227)^2 + (3.94 - 3.7017)^2 + (3.00 - 3.3176)^2 \]

Calculating each term:

\[ = 0.0635 + 0.0238 + 0.3168 + 0.0411 + 0.0568 + 0.1002 \]

Summing these values gives:

\[ \text{SSE} = 0.6022 \]

Final Answer