Added Enhancements and features

CLOCKS Multiple Regression and Interaction Model.R

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+# Set the working directory to the desired path
+setwd()
+dir()
+
+
+CLOCKS = read.table(file="GFCLOCKS.txt", header=TRUE)
+ls()
+dimnames(CLOCKS)
+CLOCKS
+
+Y = CLOCKS[,"PRICE"]
+X1 = CLOCKS[,"AGE"]
+X2 = CLOCKS[,"NUMBIDS"]
+n = length(Y)
+
+print(n)
+
+plot(X1,Y,xlim=c(100,200),ylim=c(500,2200),xlab="Age of clock",ylab = "Price of clock")
+plot(X2,Y,xlim=c(5,20),ylim=c(500,2200),xlab="No of bidders",ylab = "Price of clock")
+
+summary(X1)
+summary(X2)
+summary(Y)
+
+#Building the multiple regression
+
+model= lm(Y~X1 + X2)
+
+summary(model)
+
+
+#pt and qt class 3/4
+# qt gives t value of alpha/2 and df. Test is 2 sided so both tails will have same value. 
+qt(0.05/2, df=29) #don't specify lower tail gives negative
+
+qt(0.05/2,df = 29, lower.tail = F) #specify lower tail gives positive
+
+#Finding CI for B1 (age of clocks) 
+#lower tail false for t to be positive
+CI95.age = c(12.74,12.74) #12.74 is B1cap value from previous output
+CI95.age[1] = CI95.age[1] - qt(0.025,df=29,lower.tail=F)*0.9047 #0.9047 is SE of B1 from previous r output
+CI95.age[2] = CI95.age[2] + qt(0.025,df=29,lower.tail=F)*8.73 #8.73 is SE of B2 from previous R output 
+CI95.age
+
+#interaction model
+
+IntModel = lm(Y~X1+X2+X1:X2)
+summary(IntModel) #Even though age is not significant (p=0.66) we keep it because interaction term x1:x2 is significant (p=1.35e-06)
+

EXECSAL2.txt

@@ -0,0 +1,101 @@
+id	Y	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10
+1	11.4436	12	15	1	240	170	1	44	5	0	21
+2	11.7753	25	14	1	510	160	1	53	9	0	28
+3	11.3874	20	14	0	370	170	1	56	5	0	26
+4	11.2172	3	19	1	170	170	1	26	9	0	24
+5	11.6553	19	12	1	520	150	1	43	7	0	27
+6	11.1619	14	13	0	420	160	1	53	9	0	27
+7	11.6457	18	18	1	290	170	1	43	7	0	22
+8	11.1927	2	17	1	200	180	1	31	10	0	26
+9	11.5954	14	13	1	560	180	1	43	7	0	23
+10	11.1360	4	16	1	230	160	1	36	10	0	25
+11	11.5327	8	18	1	540	150	1	39	8	1	21
+12	11.5268	19	15	1	90	180	1	47	7	1	30
+13	11.9144	23	16	1	560	180	1	47	7	1	23
+14	10.9526	5	15	0	470	150	1	44	7	1	21
+15	11.3783	3	16	1	340	190	1	33	6	1	29
+16	11.7830	22	17	1	70	200	1	50	7	1	22
+17	11.4109	24	14	0	160	180	1	49	6	1	26
+18	11.6579	22	16	1	160	190	1	51	9	1	25
+19	11.5405	13	18	1	110	180	1	33	7	1	24
+20	11.8629	21	16	1	410	180	1	59	7	0	24
+21	11.4175	10	13	1	370	190	1	49	7	0	26
+22	11.2037	11	12	1	180	170	1	39	5	0	25
+23	11.5229	12	19	1	60	200	1	39	7	0	24
+24	11.3551	10	19	1	60	180	1	37	8	0	27
+25	11.8372	26	17	1	110	200	1	48	9	0	24
+26	11.3181	7	15	1	280	190	1	45	6	0	23
+27	11.3563	7	19	1	110	180	1	29	10	0	23
+28	11.2292	10	19	0	300	170	1	41	6	0	23
+29	11.3794	23	14	0	220	170	1	53	6	0	27
+30	11.7527	12	15	1	570	200	1	41	9	0	26
+31	11.2910	6	16	1	240	180	1	33	9	0	25
+32	11.4175	15	16	0	300	150	1	38	6	0	25
+33	11.6046	15	18	1	260	170	1	41	8	0	22
+34	11.1662	8	13	1	150	160	1	37	5	0	29
+35	11.5560	18	19	0	350	160	1	38	10	0	29
+36	11.1732	2	13	1	370	190	1	26	6	0	21
+37	11.3551	13	14	1	150	160	1	52	10	0	21
+38	11.3998	12	17	0	480	190	1	33	9	0	20
+39	11.7345	21	15	1	310	180	1	52	7	0	22
+40	10.6643	3	12	0	340	150	1	23	7	0	25
+41	11.7361	20	16	1	520	160	1	43	6	0	28
+42	11.7134	20	19	1	200	170	1	44	9	0	26
+43	11.5815	20	17	0	490	160	1	40	5	0	30
+44	11.0186	1	15	0	570	180	1	30	8	0	30
+45	10.9988	2	17	1	70	160	1	37	6	0	23
+46	11.4690	9	17	1	300	160	1	37	10	0	20
+47	11.3574	11	17	0	190	160	1	41	6	0	25
+48	11.3953	21	13	0	500	160	1	47	8	0	24
+49	11.8706	20	20	1	390	170	1	47	6	0	21
+50	11.6009	17	16	0	520	180	0	49	9	0	24
+51	11.9621	24	12	1	530	200	0	60	9	0	23
+52	11.0837	2	17	0	590	190	0	28	9	0	27
+53	11.5703	9	13	1	560	170	0	45	8	0	22
+54	11.2159	2	18	0	600	190	0	38	6	0	23
+55	11.2810	13	12	0	390	170	0	48	8	0	24
+56	11.5768	14	18	1	110	170	0	53	9	0	26
+57	11.5750	18	13	1	190	190	0	55	10	0	25
+58	11.2567	10	14	1	110	160	0	34	9	0	30
+59	11.7707	21	13	1	430	190	0	59	9	0	26
+60	11.3218	11	14	0	440	150	0	31	8	0	23
+61	11.7448	26	15	1	210	190	0	54	7	0	27
+62	11.7110	22	18	1	320	160	0	57	5	0	22
+63	11.4742	3	16	1	560	180	0	38	10	0	29
+64	11.7668	17	18	1	450	190	0	53	8	0	24
+65	11.1872	2	16	1	410	180	0	35	6	0	24
+66	10.9819	4	18	0	70	150	0	43	6	0	20
+67	11.2810	8	17	1	90	190	0	34	8	0	25
+68	11.4731	13	15	1	290	160	0	33	6	0	23
+69	11.4606	3	18	1	530	180	0	27	8	0	24
+70	11.3964	13	16	0	420	170	0	47	8	0	25
+71	11.5973	25	19	0	150	200	0	49	10	0	28
+72	11.4648	11	15	1	500	190	0	44	8	0	21
+73	11.1732	2	17	0	430	190	0	36	8	0	20
+74	12.0634	26	17	1	570	190	0	49	6	0	29
+75	11.5806	20	20	1	90	150	0	59	9	0	27
+76	11.5129	19	12	1	340	160	0	54	9	0	22
+77	11.5199	12	13	1	440	170	0	41	8	0	27
+78	11.9369	22	18	1	500	160	0	55	7	0	24
+79	11.4648	13	13	0	570	180	0	37	6	0	27
+80	11.2554	2	15	1	560	190	0	34	10	0	22
+81	11.3457	15	14	1	160	170	0	54	9	1	25
+82	11.4360	12	13	1	390	190	0	35	6	1	24
+83	11.3609	13	19	0	370	200	0	40	7	1	29
+84	11.2823	5	17	1	330	160	0	40	6	1	22
+85	11.2910	8	17	0	560	170	0	42	7	1	25
+86	11.6448	21	20	0	590	180	0	46	8	1	27
+87	11.2709	5	16	1	290	200	0	28	9	1	24
+88	11.3771	9	18	0	440	180	0	37	7	1	28
+89	11.5415	19	15	0	480	190	0	42	10	1	28
+90	11.6639	23	19	1	130	150	0	55	9	0	24
+91	10.8493	3	12	0	440	190	0	38	10	0	22
+92	11.5759	13	19	1	310	150	0	51	6	0	29
+93	11.5991	22	17	0	370	200	0	55	10	0	29
+94	11.1065	9	12	0	180	160	0	39	7	0	22
+95	11.6182	7	19	1	520	200	0	40	10	0	22
+96	11.3278	10	18	0	90	180	0	34	10	0	28
+97	11.9798	25	18	1	590	160	0	64	10	0	21
+98	11.7159	10	19	1	480	200	0	48	5	0	26
+99	11.1169	3	19	1	80	160	0	27	7	0	28
+100	11.4917	16	17	0	380	160	0	50	7	0	29

EXPRESS.txt

@@ -0,0 +1,21 @@
+Weight	Distance	Cost
+5.90	47	2.6
+3.20	145	3.9
+4.40	202	8.0
+6.60	160	9.2
+0.75	280	4.4
+0.70	80	1.5
+6.50	240	14.5
+4.50	53	1.9
+0.60	100	1.0
+7.50	190	14.0
+5.10	240	11.0
+2.40	209	5.0
+0.30	160	2.0
+6.20	115	6.0
+2.70	45	1.1
+3.50	250	8.0
+4.10	95	3.3
+8.10	160	12.1
+7.00	260	15.5
+1.10	90	1.7

EXPRESS_nested_models.R

@@ -0,0 +1,50 @@
+#set directory
+setwd()
+dir()
+
+#load data
+del = read.table(file="EXPRESS.txt", header=TRUE)
+ls()
+dimnames(del)
+del
+
+#get vectors of variables
+y = del[,"Cost"] #other way of writing: x1 = del[,1] meaning column 1 of data
+x1 = del[,"Weight"]
+x2 = del[,"Distance"]
+n = length(Y)
+n
+
+#make vectors for remaining variables-square terms
+x1sq = x1^2
+x2sq = x2^2
+
+#Fit 2 models
+ReducedModel = lm(y~x1+x2+x1:x2)
+
+CompleteModel = lm(y~x1+x2+x1sq+x2sq+x1:x2)
+
+summary_R=summary(ReducedModel)
+summary_C=summary(CompleteModel)
+
+#degree of freedom
+
+df_SSE_R = length(y)-3-1 # 3 because 3 predictors-x1,x2,x1:x2
+df_SSE_C = length(y)-5-1
+
+# Finding SSE (SSE is sigma^2 * df)
+
+SSE_R = summary_R$sigma^2*df_SSE_R
+SSE_C = summary_C$sigma^2*df_SSE_C
+
+# Finding F stat
+
+F_stat = (SSE_R-SSE_C)/(5-3)/(SSE_C/df_SSE_C)
+
+# Finding p value
+
+pf(F_stat, df1=2, df2=df_SSE_C, lower.tail = F) #Lower tail false because test is one sided
+
+# Doing the comparison of models directly using code
+
+anova(ReducedModel, CompleteModel)

Executive_data_variable_screening.R

@@ -0,0 +1,60 @@
+#EXAUSTIVE SEARCH VARIABLE SCREENING
+
+#leaps does 'exhaustive search' for us
+library(leaps)
+
+#set directory
+setwd("C:/Users/chawl/OneDrive - University of Cincinnati/Prissha/SPRING24/PROB STAT 2")
+dir()
+
+#load data
+exsal = read.table(file="EXECSAL2.txt", header=TRUE)
+ls()
+
+dimnames(exsal)
+
+Y=exsal[,"Y"]
+X1=exsal[,"X1"]
+X2=exsal[,"X2"]
+X3=exsal[,"X3"]
+X4=exsal[,"X4"]
+X5=exsal[,"X5"]
+X6=exsal[,"X6"]
+X7=exsal[,"X7"]
+X8=exsal[,"X8"]
+X9=exsal[,"X9"]
+X10=exsal[,"X10"]
+
+#conducting the exhaustive search: we get 10 models
+CandModels = regsubsets(Y~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10,data=exsal,nvmax=10,nbest=1)
+
+
+# Compute r^2, adj r^2, cp for these 10 models
+ModelSummary=summary(CandModels)
+Rsq = ModelSummary$rsq
+adjRsq = ModelSummary$adjr2
+Cp=ModelSummary$cp
+
+#display as table, round to 2 decimals
+round(rbind(Rsq,adjRsq,Cp),2)
+
+#build the 3 chosen models-4,5,6
+best4pred = lm(Y~X1+X2+X3+X4,data=exsal)
+best5pred = lm(Y~X1+X2+X3+X4+X5,data=exsal)
+best6pred = lm(Y~X1+X2+X3+X4+X5+X9,data=exsal)
+
+#conduct anova test for these models 4 and 5
+anova(best4pred,best5pred)
+
+#5 was better from last anova, so run anova for 5 and 6
+anova(best5pred,best6pred)
+
+#SO 5 IS MOST SIGNIFICANT, CHECK BETA VALUES
+best5pred$coefficients
+
+#Just for backup compare 5 and 6
+anova(best5pred,best6pred)
+
+#We confirm that 5 was more significant 
+
+

GFCLOCKS.txt

@@ -0,0 +1,33 @@
+AGE	NUMBIDS	PRICE	AGE-BID
+127	13	1235	1651
+115	12	1080	1380
+127	7	845	889
+150	9	1522	1350
+156	6	1047	936
+182	11	1979	2002
+156	12	1822	1872
+132	10	1253	1320
+137	9	1297	1233
+113	9	946	1017
+137	15	1713	2055
+117	11	1024	1287
+137	8	1147	1096
+153	6	1092	918
+117	13	1152	1521
+126	10	1336	1260
+170	14	2131	2380
+182	8	1550	1456
+162	11	1884	1782
+184	10	2041	1840
+143	6	845	858
+159	9	1483	1431
+108	14	1055	1512
+175	8	1545	1400
+108	6	729	648
+179	9	1792	1611
+111	15	1175	1665
+187	8	1593	1496
+111	7	785	777
+115	7	744	805
+194	5	1356	970
+168	7	1262	1176