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:
- How does MSE relate to model accuracy?
- What does R-squared signify in regression models?
- How do we interpret the relationship between MSE and model fit?
- What happens to R-squared when MSE is high?
- 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.
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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
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