Class Analysis Review

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
Model Fit
Source SS df MS
Number of obs 420 --------------------
----------------------- F( 3, 416)
107.45 Model 66409.8837 3
22136.6279 Prob gt 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 Pgtt 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
Estimated Coefficients
Source SS df MS
Number of obs 420 --------------------
----------------------- F( 3, 416)
107.45 Model 66409.8837 3
22136.6279 Prob gt 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 Pgtt
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 gt chi2 0.0000
7
Outlier Analysis
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 ---------------------
--------------------------------------------------
-----
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