Consider the following monthly revenue data for an up-and-coming cyber security company.



Sales DataMonthRevenue (Thousands of Dollars)MonthRevenue (Thousands of Dollars)

11

326326

99

789789

22

539539

1010

817817

33

527527

1111

829829

44

579579

1212

845845

55

635635

1313

857857

66

683683

1414

851851

77

699699

1515

855855

88

707707



The summary output from a regression analysis of the data is also provided.



Regression StatisticsMultiple R

0.9382049670.938204967

R Square

0.8802285590.880228559

Adjusted R Square

0.8710153710.871015371

Standard Error

56.426467656.4264676

Observations

1515




ANOVAdfdfSSSSMSMSFFRegression

11

304,194.432143304,194.432143

304,194.432143304,194.432143

95.5400652895.54006528

Residual

1313

41,391.30119041,391.301190

3183.9462453183.946245

Total

1414

345,585.733333345,585.733333




CoefficientsStandard Errortt StatP-valueIntercept

438.84761905438.84761905

30.6597818830.65978188

14.3134618814.31346188

2.45722E-092.45722E-09

Month

32.9607142932.96071429

3.372126423.37212642

9.7744598469.774459846

2.34292E-072.34292E-07

Step 2 of 3 :  

What is the mean square error for the model shown in the output? Round to four decimal places, if necessary.

The Mean Square Error (MSE) is a measure of the average squared difference between the observed actual outcomes and the outcomes predicted by the model. It is calculated by dividing the sum of squares for the residuals (SS Residual) by the degrees of freedom for the residuals (df Residual).

### Formula:
\[
\text{MSE} = \frac{\text{SS Residual}}{\text{df Residual}}
\]

From the provided output:
- SS Residual (also known as Residual Sum of Squares) = 41,391.301190
- df Residual = 13

### Calculation:
\[
\text{MSE} = \frac{41,391.301190}{13} = 3,183.946245
\]

Since the value is already calculated and rounded in the output, the Mean Square Error (MSE) for the model is:

\[
\text{MSE} = 3,183.9462 \text{ (rounded to four decimal places)}
\]

This value represents the average squared difference between the observed revenue values and those predicted by the regression model.

Would you like more details or have any other questions?

---

**Next Steps:**
1. How does MSE impact the accuracy of the model?
2. What is the difference between MSE and RMSE?
3. How can we reduce the MSE in a regression model?
4. What is the significance of the coefficients in the regression output?
5. How does the R-squared value relate to MSE?
6. Can high MSE values indicate overfitting?
7. What are some common causes of high MSE?
8. How does MSE compare with other error metrics like MAE?

**Tip:** The lower the MSE, the better the model fits the data. However, always consider other metrics like R-squared and residual plots to get a full picture of model performance.

Learn how to calculate Mean Square Error (MSE) for regression analysis using provided data and formulas. Understand the significance of MSE in assessing model accuracy. Suitable for advanced college-level students and professionals.

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