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# Applied Linear Regression 22S 152

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This 3 page Class Notes was uploaded by Cullen Conn on Friday October 23, 2015. The Class Notes belongs to 22S 152 at University of Iowa taught by Rhonda DeCook in Fall. Since its upload, it has received 29 views. For similar materials see /class/228074/22s-152-university-of-iowa in Natural Sciences and Mathematics at University of Iowa.

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Date Created: 10/23/15

228152 Multiple Regression continued Lecture 7 Sept 27 2002 Kate Cowles 374 SH kcowles stat uiowaedu 3 partial F test or increment to R2 tests a ls the partial effect of several indepenr dent variables signi cant in explaining the outcome variable given the rest of the varir ables in the model b called a joint or compound hypothesis 2 There are three types of tests we can perform in multiple regression 1 omnibus F test a ls the regression model useful in explaining the outcome variable 2 individual 75 tests a ls the partial effect of each independent variable signi cant in explaining the out come variable given the other variables in the model b assumes that other coef cients are unrer stricted Partial F tests Increment to R2 Tests 0 Find out if a group of predictors together in uence outcome 0 Test the addition of a group of predictors eg seasonal effects socioeconomic condir tions demographic conditions 0 Can be used only to compare nested mod els H0 Not all of the predictor variables are needed in the regression equa tion ltgt some of the ls 0 H of them HA AllKofthe 7s3 0 test statistic FTJLTK RSS I ECZUCECZ model 7 RSSqu model H 333 full modeln K Example dataset How 1960 crime rate is pre Do unemp1 and unemp2 together substanr dicted by various variables in 47 US s tates tially improve our ability to predict crime rate7 7 7 compared to a model using only Wlth 7 rate of offenses reported to police per million population age14 the number of males of age 14r24 per 1000 population south Indicator variable for Southern states 0 Mogt 1 Yes model uc Mean o years of schooling x 10 for persons of age 25 or older polex60 1960 per capita expenditure on police by state and local governme at peiexee 1959 per eepite expenditure on peiiee by me eee ieeei geeeme Tate o 1 wlth 2 unemp1 3 unemp2 labor Labor force parti ipation rate per 1000 Civilian urban males age 14r24 males number of males p r 1000 females State population size hundred tho s nu the number of nonwhites per 1000 population RBduced mOdele unemp1 Unemployment rate of urban males per 1000 of age 14r24 unemp2 Unemployment ra e of an males per 1000 f 35r39 gtk gtk wlt e ian value of transferable goods and assets or family income in tens of rate 0 2 the number of families per 1000 earning below 12 the median income H0 I 51 53 0 HA either l or g or both 71 0 proc reg data crime proc reg data crime model rate ulth model rate ulth unemp1 unemp2 run un Dependent Variable RATE Dependent Variable rate Analysis of Variance Analysis of Variance of ean Sum of Mean Source DF Squares Square F Value FrobgtF Source DF Squares Square F Value Fr gt F Model 1 1340152160 1340152160 10334 00019 Model 3 19322 644055477 560 00025 Error 45 5540 5 00 123123344 rror 43 49433 115037470 c total 4 6330927660 Corrected total 46 63309 R00 is 3503965 Rrsquare 01943 Dep Mean 9050351 Adj Rrsq 01769 Root MSF 3392454 Rquuare 02303 cV 3376945 Dependent Mean 9050351 Adj 3qu 02306 Coeff Var 743216 Farameter Fstimates Farameter Standar r for H0 Farameter Fstimates Variable DF Estimate Frror Farameter0 Frob gt ltl Farameter Standard 1111133031 1 r2423261 2363133637 r0035 09323 Variable DF Fstimate Frror t Value Fr gt ltl wlra 1 0176393 0 05361336 3 299 00019 Intercept 1 1513621 37 53529 0 40 06373 ulth 1 0 16306 005209 323 00024 unemp1 1 r033547 041633 200 00514 unemp2 1 196562 039271 220 00331 H 2 how many fewer predictor variables in reduced model than in full model K 4 number of s in full model RSSTeduced model 7 RSSqu model H FHK n RSSfull model n 7 K F2 5540775749488 2 47 4 49488 48 295988 115088 2 572 Other Inferences The same kinds of inferences can be drawn from the MR model as were from the SLR model 0 test of overall fit7 F test 0 test and Cls for individual partial effects7 i i tnik iaQ X 981 Now 6398 depends on r variability of Ys around regression line 7 how spread out the X variable is 7 how highly correlated X variables are with each other 10 Compare to F423 distribution in Table A4 in text 05 cutoff for F420 323 for F620 315 So 05 cutoff for F423 iis between 315 and 323 2572 is lt either one So the two variables unemp 1 and uneme taken together are not significant at the 05 level 0 Cl for mean of all Yls with a particular set of X values YX i tniK iaQ X where YX B0 B1Xf BQX kXI and ampYX can be obtained from SAS output clm Cl is narrowest when each X equals its respective mean 0 prediction interval for individual new Y with a particular set of X values Ynew i tnik iaQ X 66771611 where Ynew Bo 31Xf B2X BkXI and 9Ynew can be obtained from SAS cli wider than corresponding Cl for mean Y

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