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from the split data. c

from the split data. c

MATLAB: An Introduction with Applications
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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9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
Samples ar Scatteved In a. Scater.. elet and not moitke a Straight li re, -0.127 A0224 -1.276 2.52 (V) 1 year Students In 10% of HS Class ART 0.099 Acceptance Rate 1st-Year Students in Top 10% of HS Class -0.341 0.088 (01) Ioviem 0.116 0.089 1.304 0.215 -0.076 0.308 Academic Reputation Score 2.075 4.018 0.516 0.614 -6.607 10.756 Student/Faculty Ratio -0.532 0.408 -1.305 0.215 -1.413 0.349 DC pendent variable : Girad Rate 30 T200 ai sldsiay anb ndependent Variables Odog ol 0 eldeh verutuba ai doin SUMMARY OUTPUT olini ods ig mi lbas alimaup obeloni (ii) % of classes of so or> Ci)% of Classes <20 ibian NOT2AM bodia n alasbut lo a Regression Statistics Multiple R (l) student leaculty 0.564 (iv) acceptance rat asmT bulox 0.821 la R Square 0.673 Adjusted R Square ratioa2 Standard Error Observations 25 ANOVA LEB.0 df SS MS F Significance F Regression 236.32 39.39 6.18 0.0012 Residual 18 114.64 6.37 AVOKA Total 24 350.96 22 Coefficients Standard Error t Stat P-value Lower 95% g Upper 95% Intercept 70.26 10.59 6.63 Or 0.00 48.01 atoT 92.51 % of Classes Under 20 0.021 0.087 0.241 0.812 -0.161 0.203 % of Classes of 50 or More alloa -0.013 0.221 -0.060 0.953 -0.478 0.452 -0.274 Too2 lo T -0.046 i -0.159 0.055 -2.907 0.009 -0.044 Acceptance Rate 1st-Year Students in Top 10% of HS Class 0.142 0.090 1.589 0.129 0.330 10.8 0.520 TA2 budT 1.278 1.947 0.656 -2.812 5.368 Academic Reputation Score 0.688 0.268 2.563 0.020 0.124 1.251 Student/Faculty Ratio a) What is heteroscedasticity? be also it means thnat the variances of sampics are unequal, H defined as the varian, ces of errers Usually, the sample points of uch In Stats Samples are scaftered Ih9 cafterelet andnot matee a b) Why is heteroscedasticity a problem? Stranght lime. 1J Distribuion is not nermal distributioribc of which the frest is hat applicaba is calculate'd in Sampie thL OLS Cstimators arent the eng all the nbiased est theiY vanance isnt the s Indecates that c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance). BLUE unich 8.A1 382080e10 L0.0 Iood 2 o T00 0 00.0 02.0 llungnaldog nlloolo teds ecge ch 2oob r a o bod e
Transcribed Image Text:Samples ar Scatteved In a. Scater.. elet and not moitke a Straight li re, -0.127 A0224 -1.276 2.52 (V) 1 year Students In 10% of HS Class ART 0.099 Acceptance Rate 1st-Year Students in Top 10% of HS Class -0.341 0.088 (01) Ioviem 0.116 0.089 1.304 0.215 -0.076 0.308 Academic Reputation Score 2.075 4.018 0.516 0.614 -6.607 10.756 Student/Faculty Ratio -0.532 0.408 -1.305 0.215 -1.413 0.349 DC pendent variable : Girad Rate 30 T200 ai sldsiay anb ndependent Variables Odog ol 0 eldeh verutuba ai doin SUMMARY OUTPUT olini ods ig mi lbas alimaup obeloni (ii) % of classes of so or> Ci)% of Classes <20 ibian NOT2AM bodia n alasbut lo a Regression Statistics Multiple R (l) student leaculty 0.564 (iv) acceptance rat asmT bulox 0.821 la R Square 0.673 Adjusted R Square ratioa2 Standard Error Observations 25 ANOVA LEB.0 df SS MS F Significance F Regression 236.32 39.39 6.18 0.0012 Residual 18 114.64 6.37 AVOKA Total 24 350.96 22 Coefficients Standard Error t Stat P-value Lower 95% g Upper 95% Intercept 70.26 10.59 6.63 Or 0.00 48.01 atoT 92.51 % of Classes Under 20 0.021 0.087 0.241 0.812 -0.161 0.203 % of Classes of 50 or More alloa -0.013 0.221 -0.060 0.953 -0.478 0.452 -0.274 Too2 lo T -0.046 i -0.159 0.055 -2.907 0.009 -0.044 Acceptance Rate 1st-Year Students in Top 10% of HS Class 0.142 0.090 1.589 0.129 0.330 10.8 0.520 TA2 budT 1.278 1.947 0.656 -2.812 5.368 Academic Reputation Score 0.688 0.268 2.563 0.020 0.124 1.251 Student/Faculty Ratio a) What is heteroscedasticity? be also it means thnat the variances of sampics are unequal, H defined as the varian, ces of errers Usually, the sample points of uch In Stats Samples are scaftered Ih9 cafterelet andnot matee a b) Why is heteroscedasticity a problem? Stranght lime. 1J Distribuion is not nermal distributioribc of which the frest is hat applicaba is calculate'd in Sampie thL OLS Cstimators arent the eng all the nbiased est theiY vanance isnt the s Indecates that c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance). BLUE unich 8.A1 382080e10 L0.0 Iood 2 o T00 0 00.0 02.0 llungnaldog nlloolo teds ecge ch 2oob r a o bod e
1st year Students In 10% of 9 The following results are from a regression where the dependent variable is GRADUATION RATE and the indenendent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE. STUDENT/EACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OFUS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. 283.0 SUMMARY OUTPUT cern Regression Statistics 12.11 0.588 Multiple R 0.346 R Square 0.044 Adjusted R Square AVOMA 4.55 Standard Error 20 Observations no 320 ANOVA MS F Significance F df S 142.0 23.7 1.15 0.391 6 Regression Residual go 268.8 20.7 saln13 ELO 19 18.0- 410.8 Total Or 80- anoe TA2 bonidmo SE80.0 E3210 t Stat 0S P-value Lower 95% Upper 95% Coefficients Standard Error 25.9 30.9 142.8 3.4 0.0 Intercept 86.8 -0.613 0.271 0.205 -0.838 0.417 -0.171 % of Classes of 50 or More 2 2AD SD0.266 quots 0.387arw-0.688in 0.503vol dPO 1.102 UTa -0.341 % of Classes Under 20 0.570 0.088 0.224 NDEAL -1.276 0.099 (01) earsogyd 20o -0.127 Acceptance Rate 1st-Year Students in Top 10% of HS Class 0.215 -0.076 0.308 0.116 0.089 1.304 0.516 0.614 -6.607 10.756 2,075 4.018 Academic Reputation Score 0.349 -0.532 0.408 -1.305 0.215 -1.413 Student/Faculty Ratio De pendent Variabe i Girad Rate gor ga n aivweliol ofT (OI O T200 at sldelay nabitcndependent Variablesoqol ed SUMMARY OUTPUT opildug ol 0= olrin vmmub e zi doilwoor NO T2Mfoorize svng toi I baa oliraup asbuta lo sno0 IT Regression Statisticsto uroa ogeva orl ASIHT oru 2sbuloxo 0.821 0.673 a adi a (i) student (eaculty ardi ai doidw Roa AOOA bas (iD of classes of so or> Multiple R shuloni R Square 0.564 (iv) acceptance rat Adjusted R Square ratio MU2 2.52 (V) 1st year students in 10% of Hs c. Standard Error Observations 25 TolquibM ANOVA LE8.0 df SS MS F Significance F Regression 6. 236.32 0.0012 JO 39.39 6.18 Residual 18 114.64 6.37 Total 24 350.96 AVOMA Coefficients Standard Error t Stat P-value Lower 95% g Upper 95S Intercent 70 26 10 C
Transcribed Image Text:1st year Students In 10% of 9 The following results are from a regression where the dependent variable is GRADUATION RATE and the indenendent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE. STUDENT/EACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OFUS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. 283.0 SUMMARY OUTPUT cern Regression Statistics 12.11 0.588 Multiple R 0.346 R Square 0.044 Adjusted R Square AVOMA 4.55 Standard Error 20 Observations no 320 ANOVA MS F Significance F df S 142.0 23.7 1.15 0.391 6 Regression Residual go 268.8 20.7 saln13 ELO 19 18.0- 410.8 Total Or 80- anoe TA2 bonidmo SE80.0 E3210 t Stat 0S P-value Lower 95% Upper 95% Coefficients Standard Error 25.9 30.9 142.8 3.4 0.0 Intercept 86.8 -0.613 0.271 0.205 -0.838 0.417 -0.171 % of Classes of 50 or More 2 2AD SD0.266 quots 0.387arw-0.688in 0.503vol dPO 1.102 UTa -0.341 % of Classes Under 20 0.570 0.088 0.224 NDEAL -1.276 0.099 (01) earsogyd 20o -0.127 Acceptance Rate 1st-Year Students in Top 10% of HS Class 0.215 -0.076 0.308 0.116 0.089 1.304 0.516 0.614 -6.607 10.756 2,075 4.018 Academic Reputation Score 0.349 -0.532 0.408 -1.305 0.215 -1.413 Student/Faculty Ratio De pendent Variabe i Girad Rate gor ga n aivweliol ofT (OI O T200 at sldelay nabitcndependent Variablesoqol ed SUMMARY OUTPUT opildug ol 0= olrin vmmub e zi doilwoor NO T2Mfoorize svng toi I baa oliraup asbuta lo sno0 IT Regression Statisticsto uroa ogeva orl ASIHT oru 2sbuloxo 0.821 0.673 a adi a (i) student (eaculty ardi ai doidw Roa AOOA bas (iD of classes of so or> Multiple R shuloni R Square 0.564 (iv) acceptance rat Adjusted R Square ratio MU2 2.52 (V) 1st year students in 10% of Hs c. Standard Error Observations 25 TolquibM ANOVA LE8.0 df SS MS F Significance F Regression 6. 236.32 0.0012 JO 39.39 6.18 Residual 18 114.64 6.37 Total 24 350.96 AVOMA Coefficients Standard Error t Stat P-value Lower 95% g Upper 95S Intercent 70 26 10 C
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