Math Problem Statement

The mean squared error (MSE) is measured in of the Y variable. The the MSE the the R-squared.

Please fill in the blanks from the choice below to complete the sentence.

a percent, higher, higher

in units, higher, lower

in units, lower, lower

a percent, lower, lower

Solution

The correct completion of the sentence is:

"The mean squared error (MSE) is measured in units of the Y variable. The lower the MSE, the higher the R-squared."

So the correct option is: in units, lower, higher.

Explanation:

  • The MSE is measured in the same units as the dependent variable (Y).
  • R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. A lower MSE generally means a better fit of the model, and consequently, a higher R-squared.

Would you like further clarification or examples on MSE or R-squared? Here are some related questions:

  1. How does MSE relate to model accuracy?
  2. What does R-squared signify in regression models?
  3. How do we interpret the relationship between MSE and model fit?
  4. What happens to R-squared when MSE is high?
  5. Can you explain the difference between MSE and RMSE?

Tip: To improve model performance, always check the MSE and consider optimizing your model to reduce this error.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Regression Analysis
Mean Squared Error (MSE)
R-squared

Formulas

MSE = (1/n) * Σ(y_i - ŷ_i)^2
R-squared = 1 - (SS_res / SS_tot)

Theorems

R-squared interpretation
MSE interpretation in model fitting

Suitable Grade Level

Grades 11-12