The significant model equation is for predicting influences on physicians' decisions to see PSRs.
Understand the Problem
The question is asking to identify the correct model equation that predicts influences on physicians' decisions to see PSRs from the provided options (A, B, C, D). Each option presents a different mathematical equation, likely representing a model in a statistical or data analysis context.
Answer
The significant model equation is $Y = 2.4 + 0.5 X_1 - 0.80 X_2 + 0.20 X_3 - 0.25 X_4 + E$.
Answer for screen readers
The significant model equation is:
$$ Y = 2.4 + 0.5 X_1 - 0.80 X_2 + 0.20 X_3 - 0.25 X_4 + E $$
Steps to Solve
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Identifying the Components of the Equations
Each option presents a linear regression model of the form: $$ Y = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4 + b_5 X_5 + E $$ where $Y$ is the dependent variable, $a$ is the intercept, $b_i$ are the coefficients, $X_i$ are the independent variables, and $E$ is the error term.
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Analyzing the Given Options
Review each of the equations provided in options A, B, C, and D. Observe the coefficients and terms for accuracy and clarity:
- Option A: $Y = 2.4 + 0.5 X_1 - 0.80 X_2 + 0.20 X_3 - 0.25 X_4 - 0.75 X_5 + E$
- Option B: $Y = -2.4 + 0.5 X_1 + 0.80 X_2 + 0.20 X_3 + E$
- Option C: $Y = 2.4 + 0.5 X_1 - 0.80 X_2 + 0.20 X_3 - 0.25 X_4 + E$
- Option D: $Y = 2.4 + 0.5 X_1 - 0.80 X_2 + 0.20 X_3 + E$
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Determining the Most Significant Equation
Compare the options to find the equation that best fits the analysis. Look for:
- Consistency in the coefficients
- Presence of all variables mentioned or affected in the context
Based on the analysis, certain coefficients and variables are either repeated or absent in options.
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Choosing the Correct Option
From the analysis of options A through D, carefully select the option that includes all terms and has coherent coefficients. For instance, choose based on the stability or appropriateness of coefficients that suggest the best predictors.
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Final Selection
After analyzing and reviewing, finalize your choice and ensure it aligns with the statistical or predictive accuracy as required.
The significant model equation is:
$$ Y = 2.4 + 0.5 X_1 - 0.80 X_2 + 0.20 X_3 - 0.25 X_4 + E $$
More Information
Option C represents the correct model because it includes all necessary predictors and maintains a consistent equation structure. In modeling contexts, it's essential to include only relevant predictors to avoid overfitting.
Tips
- Ignoring coefficients: Ensure to check and understand the implications of coefficients in each option.
- Misreading signs: Be careful about the signs of coefficients (negative vs. positive) which can significantly alter the interpretation of the model.
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