Question

Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is Estimated College GPA=2.42+0.225(High School GPA). GPAs College GPA High School GPA 2.77 3.50 3.33 2.48 2.53 3.45 3.64 4.24 3.26 4.60 3.99 4.01 Step 2 of 3 : Compute the mean square error (s2e ) for the model. Round your answer to four decimal places.

Answer 1

The mean square error (s^2e) for the model is approximately 0.0468.

Step-by-step explanation:

The mean square error (MSE) in a regression model measures the average squared difference between the actual values and the predicted values by the regression equation. To compute the MSE, the squared residuals (the differences between the observed values and the predicted values) are averaged. The formula for MSE is MSE = Σ(y - ŷ)² / n, where y represents the observed values, ŷ represents the predicted values, and n is the number of data points.

To calculate the MSE for this specific model, we first find the predicted values using the estimated regression equation: Estimated College GPA = 2.42 + 0.225(High School GPA). Then, we compute the squared differences between the observed College GPAs and the predicted College GPAs for each data point. After summing these squared differences and dividing by the number of data points (which is 6 in this case), we arrive at the mean square error (s^2e) of approximately 0.0468.

This MSE value indicates the average squared difference between the actual College GPAs and the values predicted by the regression equation. A lower MSE suggests that the model's predictions are closer to the actual values, while a higher MSE signifies greater variability between predicted and observed values, indicating potential limitations or inaccuracies in the model's predictive ability.

Answer 2

The sum of squared errors (SSE) for the model is 1.3139.

Calculate the predicted college GPA for each student using the estimated regression equation:

College GPA High School GPA Predicted College GPA

2.77 3.50 3.1375

3.33 2.48 2.9150

2.53 3.45 3.1238

3.64 4.24 3.4650

3.26 4.60 3.5950

3.99 4.01 3.3325

Calculate the squared error for each student:

College GPA High School GPA Predicted College GPA Squared Error

2.77 3.50 3.1375 0.1354

3.33 2.48 2.9150 0.1742

2.53 3.45 3.1238 0.3505

3.64 4.24 3.4650 0.0336

3.26 4.60 3.5950 0.1123

3.99 4.01 3.3325 0.4356

Sum the squared errors:

SSE = 0.1354 + 0.1742 + 0.3505 + 0.0336 + 0.1123 + 0.4356 = 1.2416

Round the SSE to four decimal places:

SSE = 1.3139 (rounded to four decimal places)