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Class Analysis Review

Class Analysis Review. Predict Test Score (testscr), using the following independent variables: Student teacher ratio (str) Expenditures per student ( expn_stu ) % students with English as a second language ( el_pct ) Run the model Evaluate the Output Draw Initial Conclusions. Multiple R.

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Class Analysis Review

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  1. Class Analysis Review • Predict Test Score (testscr), using the following independent variables: • Student teacher ratio (str) • Expenditures per student (expn_stu ) • % students with English as a second language (el_pct) • Run the model • Evaluate the Output • Draw Initial Conclusions

  2. Multiple R Model Fit Source | SS df MS Number of obs = 420 -------------+------------------------------ F( 3, 416) = 107.45 Model | 66409.8837 3 22136.6279 Prob > F = 0.0000 Residual | 85699.7099 416 206.008918 R-squared = 0.4366 -------------+------------------------------ Adj R-squared = 0.4325 Total | 152109.594 419 363.030056 Root MSE = 14.353 ------------------------------------------------------------------------------ testscr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- str | -.2863992 .4805232 -0.60 0.551 -1.230955 .658157 expn_stu | .0038679 .0014121 2.74 0.006 .0010921 .0066437 el_pct | -.6560227 .0391059 -16.78 0.000 -.7328924 -.5791529 _cons | 649.5779 15.20572 42.72 0.000 619.6883 679.4676 ------------------------------------------------------------------------------

  3. Standardized coefficients indicate relative magnitudes of effect Estimated Coefficients Source | SS df MS Number of obs = 420 -------------+------------------------------ F( 3, 416) = 107.45 Model | 66409.8837 3 22136.6279 Prob > F = 0.0000 Residual | 85699.7099 416 206.008918 R-squared = 0.4366 -------------+------------------------------ Adj R-squared = 0.4325 Total | 152109.594 419 363.030056 Root MSE = 14.353 ------------------------------------------------------------------------------ testscr | Coef. Std. Err. t P>|t| Beta -------------+---------------------------------------------------------------- str | -.2863992 .4805232 -0.60 0.551 -.0284367 expn_stu | .0038679 .0014121 2.74 0.006 .1286916 el_pct | -.6560227 .0391059 -16.78 0.000 -.6295997 _cons | 649.5779 15.20572 42.72 0.000 . ------------------------------------------------------------------------------

  4. Residual Distribution

  5. Residuals by Predicted Values

  6. Heteroscedasticity Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of testscr chi2(1) = 17.67 Prob > chi2 = 0.0000

  7. predict yhat predict e, resid gsort e list dist_cod testscr str expn_stu el_pct yhat e in 1/5 +----------------------------------------------------------------------------+ | dist_cod testscr str expn_stu el_pct yhat e | |----------------------------------------------------------------------------| 1. | 62042 605.55 21.40625 5580.147 12.40876 656.8903 -51.3402 | 2. | 70409 635.6 14 6653.031 0 671.3016 -35.70165 | 3. | 70417 635.45 15.27273 6313.374 0 669.6234 -34.17335 | 4. | 72181 616.3 20.00822 4818.613 20.53388 649.0148 -32.71485 | 5. | 62331 612.5 19.94737 5355.548 30.07916 644.8472 -32.34716 | +----------------------------------------------------------------------------+ Outlier Analysis gsort -e list dist_cod testscr str expn_stu el_pct yhat e in 1/5 +---------------------------------------------------------------------------+ | dist_cod testscr str expn_stu el_pct yhat e | |---------------------------------------------------------------------------| 1. | 69518 706.75 17.86263 5741.463 4.726101 663.5691 43.18091 | 2. | 69682 700.3 18.86534 5392.639 2.050406 663.688 36.61204 | 3. | 68957 704.3 16.47413 7290.339 5.995935 669.1246 35.17543 | 4. | 61747 696.55 19.15261 5592.765 1.962865 664.4373 32.11281 | 5. | 61713 694.8 20.12881 5230.877 .8936293 663.4594 31.3407 | +---------------------------------------------------------------------------+

  8. Conclusions? • Model fit? • Better than using mean? • Percent variance explained? • Hypothesis tests? • Magnitude of estimated coefficients? • Residual analysis • Linearity? • Homoscedasticity? • Outliers?

  9. Next Week • Brief Review • Distribution of Exams

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