Please help me better understand word problem. A researcher was investigating variables that might be associated with the academic performance of high school students. The data included the average Math SAS score of all high school seniors in the city that took the exam (labeled as the variable SAT-M), the average number of dollars per pupil spent on education by the city (labeled as the variable $Per Pupil), and the percentage of high school seniors in the city that took the exam (labeled as the variable %Taking). The researcher ran the following multiple linear regression model as SAT-M=Beta0 + Beta1($Per Pupil) + Beta2(%Taking). This model was fit to the data using the method of least-squares, results shown inside of table within photo. What proportion of the variation in the variable SAT-M is explained by the explanatory variables $Per Pupil and %Taking? ### Statistical Analysis Results#### Table SummaryThis table presents the results of a statistical analysis, breaking down the sources of variation and parameter estimates within the model.#### Source of Variation- **Model** - **Sum of Squares**: 45915.0 - **Degrees of Freedom (df)**: 2- **Error** - **Sum of Squares**: 13835.1 - **Degrees of Freedom (df)**: 50#### Parameter Estimates- **Constant** - **Parameter Estimate**: 514.652 - **Standard Error**: 10.30- **$Per Pupil** - **Parameter Estimate**: 0.00639 - **Standard Error**: 0.0025- **%Taking** - **Parameter Estimate**: -1.49221 - **Standard Error**: 0.1419### ExplanationThe table is divided into two main sections: the source of variation and the parameter estimates. - **Source of Variation**: This includes the model's sum of squares and the sum of the squares for error, along with their respective degrees of freedom. The sum of squares is a measure of the variability within data points as explained by the model.- **Parameter Estimates**: This section includes estimates for the constants and the independent variables, along with their standard errors, indicating the precision of these estimates. The parameters include a constant, the effect on per pupil spending ($Per Pupil), and the percentage of students taking the program (%Taking).Such results are typically used to assess the fit and predictive power of statistical models.

Answered: A researcher was investigating…

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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Please help me better understand word problem. A researcher was investigating variables that might be associated with the academic performance of high school students. The data included the average Math SAS score of all high school seniors in the city that took the exam (labeled as the variable SAT-M), the average number of dollars per pupil spent on education by the city (labeled as the variable $Per Pupil), and the percentage of high school seniors in the city that took the exam (labeled as the variable %Taking). The researcher ran the following multiple linear regression model as SAT-M=Beta0 + Beta1($Per Pupil) + Beta2(%Taking). This model was fit to the data using the method of least-squares, results shown inside of table within photo.

What proportion of the variation in the variable SAT-M is explained by the explanatory variables $Per Pupil and %Taking?