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## You wanted to improve the model from question two and have decided to include a new variable, percentage of English learners (EL PCT). SUMMARY OUTPUT Regression Statistics Multiple R 0.653017122 R Square 0.426431361 Adjusted R Square 0.423680433 Standard Error 14.46448496 Observations 420 ANOVA                               df    SS                  MS                  F Regression            2      64864.3011   32432.15055 155.0135989 Residual                417 87245.29254   209.221325 Total                      419 152109.5936                           Coefficients                                                 Standard                                                    Error            t Stat       P-value Intercept            686.0322487 7.411312484 str                     -1.101295889 0.380278316 el_pct                -0.649776777 0.039342549 (a) Is this second model a better or worse model than the one in question 2? Why? (b) Are all the signs of the variables as expected? State reason.  (c) A colleague of yours believes that English learners is not significant in determining test scores. Conduct a hypothesis test to prove whether this is true or not assuming =0.05 i.e myu= 0.05   As question 2 is: Question 2  The following regression output was obtained. The regression model is Test scores on student teacher ratio. When your research assistant cut and pasted the results for you, there were several vital pieces of information missing. See output below: SUMMARY OUTPUT Regression Statistics Multiple R 0.226362751 R Square (a) Adjusted R Square 0.048970335 Standard Error 18.5809675 Observations 420 ANOVA                            df            SS                            MS                           F Regression       1                        7794.110041    7794.110041    22.57511055 Residual          418                      144315.4836     345.2523531 Total               419                       (b)                                Coefficients                                                         Standard                                                         Error              t Stat     P-value Intercept                   698.9329523  9.467491444 str                            -2.279808287  0.479825567   (c)

Question 3
You wanted to improve the model from question two and have decided to include a new
variable, percentage of English learners (EL PCT).

SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.653017122
R Square 0.426431361
Standard Error 14.46448496
Observations 420

ANOVA
df    SS                  MS                  F
Regression            2      64864.3011   32432.15055 155.0135989
Residual                417 87245.29254   209.221325
Total                      419 152109.5936

Coefficients
Standard
Error            t Stat       P-value
Intercept            686.0322487 7.411312484
str                     -1.101295889 0.380278316
el_pct                -0.649776777 0.039342549

(a) Is this second model a better or worse model than the one in question 2? Why?
(b) Are all the signs of the variables as expected? State reason.
(c) A colleague of yours believes that English learners is not significant in determining
test scores. Conduct a hypothesis test to prove whether this is true or not assuming
=0.05 i.e myu= 0.05

As question 2 is:

Question 2
The following regression output was obtained. The regression model is Test scores on
student teacher ratio. When your research assistant cut and pasted the results for you, there
were several vital pieces of information missing. See output below:

SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.226362751
R Square (a)
Standard Error 18.5809675
Observations 420
ANOVA
df            SS                            MS                           F
Regression       1                        7794.110041    7794.110041    22.57511055
Residual          418                      144315.4836     345.2523531
Total               419                       (b)

Coefficients
Standard
Error              t Stat     P-value
Intercept                   698.9329523  9.467491444
str                            -2.279808287  0.479825567   (c)

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