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R² and model fit. Because the coefficient of determination, R², always increases when a new independent variable is added to the model, it is tempting to include many variables in the model in order to force R² to be near 1. However, doing so reduces the number of degrees of freedom available for estimating o², which adversely affects our ability to make reliable inferences. Suppose you want to use 18 psychological and sociological factors to predict a student's Scholastic Assessment Test (SAT) score. You fit the model Y = Bo + B₁x₁ + B₂x₂ + ... + B17x17 + B18x18 + € where Y=SAT score and x₁, x2, ..., 17, 18 are the psychological and sociological factors. 1, Only 20 years of data (n = 20) are used to fit the model, and you obtain R² = 0.95. Test to see whether this impressive looking R² is large enough for you to infer that the model is useful-that is, that at least one term in the model is important in predicting SAT scores. Use a = 0.05.

R² and model fit. Because the coefficient of determination, R², always increases when a new independent variable is added to the model, it is tempting to include many variables in the model in order to force R² to be near 1. However, doing so reduces the number of degrees of freedom available for estimating o², which adversely affects our ability to make reliable inferences. Suppose you want to use 18 psychological and sociological factors to predict a student's Scholastic Assessment Test (SAT) score. You fit the model Y = Bo + B₁x₁ + B₂x₂ + ... + B17x17 + B18x18 + € where Y=SAT score and x₁, x2, ..., 17, 18 are the psychological and sociological factors. 1, Only 20 years of data (n = 20) are used to fit the model, and you obtain R² = 0.95. Test to see whether this impressive looking R² is large enough for you to infer that the model is useful-that is, that at least one term in the model is important in predicting SAT scores. Use a = 0.05.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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R² and model fit. Because the coefficient of determination, R², always increases when a new independent variable is added to the model, it is tempting to include many variables in the model in order to force R2 to be near 1. However, doing so reduces the number of degrees of freedom available for estimating o2, which adversely affects our ability to make reliable inferences. Suppose you want to use 18 psychological and sociological factors to predict a student's Scholastic Assessment Test (SAT) score. You fit the model Y = Bo + B₁x1 + B₂x2 + ... + B17x17 + B18x18 + € where Y=SAT score and ₁, 2, ..,17,18 are the psychological and sociological factors. Only 20 years of data (n = 20) are used to fit the model, and you obtain R² = 0.95. Test to see whether this impressive looking R² is large enough for you to infer that the model is useful-that is, that at least one term in the model is important in predicting SAT scores. Use a = 0.05.
Transcribed Image Text:R² and model fit. Because the coefficient of determination, R², always increases when a new independent variable is added to the model, it is tempting to include many variables in the model in order to force R2 to be near 1. However, doing so reduces the number of degrees of freedom available for estimating o2, which adversely affects our ability to make reliable inferences. Suppose you want to use 18 psychological and sociological factors to predict a student's Scholastic Assessment Test (SAT) score. You fit the model Y = Bo + B₁x1 + B₂x2 + ... + B17x17 + B18x18 + € where Y=SAT score and ₁, 2, ..,17,18 are the psychological and sociological factors. Only 20 years of data (n = 20) are used to fit the model, and you obtain R² = 0.95. Test to see whether this impressive looking R² is large enough for you to infer that the model is useful-that is, that at least one term in the model is important in predicting SAT scores. Use a = 0.05.
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