Part 1: RKO Movie Earnings and Costs

Dataset: rko_film_19301941.dat

Source: J. Sedgwick (1994). "Richard B. Jewell's RKO Film Grosses, 1929-1951:The C.J. Trevlin Ledger: A Comment", Historical Journal of Film, Radio &Television, Vol.14, Issue 1, p. 51

Description: Costs and Earnings of 155 RKO movies from 1930-1941.

Variables/Columns

Film 1-25

Re-release dummy 33 /* 1=Re-release, 0 if not

Production costs ($1000s) 36-41

Domestic Revenue ($1000s) 44-49

Foreign Revenue ($1000s) 53-57

Total Revenue ($1000s) 61-65

Profits ($1000s) 68-73

Distribution Cost($1000s) 76-81

Dist Cost/Revenue 83-88

Dist Cost/Prod Cost 91-97

Year 100-104

100*Profit/(Prod+dist cost) 106-111

A study reported various costs and revenues for movies released by RKO during the years 1930-1941. Fit linear regression models relating Total Revenue to Total Cost (Distribution + Production) by completing the following parts.

p.1.a. Fit a simple linear regression model based on ordinary least squares. Give the fitted equation, estimated standard errors, and the estimate ofs

p.1.b. Plot the residuals, absolute residuals, and squared residuals versus the fitted values

p.1.c. Obtain the correlations between the absolute residuals and fitted values and squared residuals and fitted values

p.1.d. Obtain the Weighted Least Squares estimatorb_Win matrix form (iteratively) based on the model that the standard deviation ofe is proportional to the mean. Give the point estimates and standard errors of the regression coefficients.

p.1.e. Using theglsfunction in thenlmepackage to obtain the generalized least squares estimates using the power relation:: Give the estimates of a, d

p.1.f. Compare the slope estimate and their standard error for Ordinary and Generalized Least Squares.

R Program to Read Data

rko.dat <- read.csv("https://www.stat.ufl.edu/~winner/data/rko_film_19301941.csv") attach(rko.dat); names(rko.dat)

totCost <- distCost+prodCost

EXAMPLE

R code

nflcomb <- read.csv("http://www.stat.ufl.edu/~winner/sta4210/mydata/nfl_combine.csv", header=TRUE) attach(nflcomb); names(nflcomb)

#### Matrix form (using lm for |e|,y-hat regressions) ###########

n <- length(Weight) X0 <- rep(1,n) X <- as.matrix(cbind(X0,Height,ArmLng,HandLng)) Y <- as.matrix(Weight) p <- ncol(X)

#### Fit original regression, and regress functions of |e| on Y-hat

b.ols <- solve(t(X) %*% X) %*% t(X) %*% Y # b=(X'X)^(-1)X'Y mse.o <- (t(Y-X%*%b.ols) %*% (Y-X%*%b.ols))/(n-p) # MSE=(Y-Xb)"(Y-Xb)/(n-p) s2.b.ols <- mse.o[1,1]*solve(t(X) %*% X) # s2{b}=MSE*(X'X)^(-1) s.b.ols <- sqrt(diag(s2.b.ols)) # s{b}=sqrt(diag(b}} t.b.ols <- b.ols/s.b.ols # t=b/s{b} p.b.ols <- 2*(1-pt(abs(t.b.ols), n-p)) # P-value

ols.out <- cbind(b.ols, s.b.ols, t.b.ols, p.b.ols) colnames(ols.out) <- c("b_ols", "Std. Error", "t*", "P(>|t*|)") rownames(ols.out) <- c("Intercept", "Height", "Arm Length", "Hand Length")

#### Plot 1) |e| vs Y-hat 2) e^2 vs Y-hat 3) sqrt(|e|) vs Y-hat yhat.ols <- X %*% b.ols e.ols <- Y - yhat.ols

par(mfrow=c(1,3)) plot(abs(e.ols) ~ yhat.ols, pch=16) abline(lm(abs(e.ols) ~ yhat.ols)) plot(e.ols^2 ~ yhat.ols, pch=16) abline(lm(e.ols^2 ~ yhat.ols)) plot(sqrt(abs(e.ols)) ~ yhat.ols, pch=16) abline(lm(sqrt(abs(e.ols)) ~ yhat.ols))

cor(abs(e.ols) , yhat.ols) cor(e.ols^2 , yhat.ols) cor(sqrt(abs(e.ols)) , yhat.ols) # Highest correlation for sqrt(|e|) with Y-hat

# Fit regression of sqrt(|e|) on Y-hat e.reg.ols <- lm(sqrt(abs(e.ols)) ~ yhat.ols) summary(e.reg.ols) s.ols <- predict(e.reg.ols) # Predicted sqrt(|e|) w.ols <- 1/s.ols^4 # WLS weights= 1/s^2 = 1/sqrt(|e|)^4

## Begin iterations to obtain WLS estimator b_w b.old <- b.ols # Start iterations with OLS estimator wm.old <- as.matrix(diag(w.ols)) # W = diagonal matrix with w_i=1/s_i^2 b.diff <- 100 # Set high starting difference num.iter <- 0 # Counter for number of iterations

# Keep iterating until (b_new-b_old)'(b_new-b_old) < .00001 while (b.diff > 0.00001) { num.iter <- num.iter+1 # Increment number of iterations # b_new = (X'WX)^(-1)X'WY b.new <- solve(t(X) %*% wm.old %*% X) %*% t(X) %*% wm.old %*% Y yhat.new <- X %*% b.new # Yhat_new = Xb_new abs.e.new <- abs(Y - yhat.new) # new |e| = Y-Yhat_new # Create new weight matrix from regression of sqrt(|e_new|) on yhat_new wm.new <- as.matrix(diag(1/predict(lm(sqrt(abs.e.new)~yhat.new))^4)) b.diff <- sum((b.new-b.old)^2) # sum of squared differences of b_new,b_old b.old <- b.new # b.old is assigned b.new wm.old <- wm.new # Old weight matrix is assigned new weight matrix }

# End of loop num.iter # Number of iterations needed

# Apply wm.new to get b.new (probably not necessary) b.new <- solve(t(X) %*% wm.new %*% X) %*% t(X) %*% wm.new %*% Y b.wls <- b.new # Obtain b.wls as result from iterative process wm.wls <- wm.new # Obtain WLS matrix from iterative process

## MSE_wls = (Y-Xb-w)'W(Y-Xb_w) mse.w <- (t(Y-X%*%b.wls) %*% wm.wls %*% (Y-X%*%b.wls))/(n-p)

# s2{b_w} = MSE*(X'WX)^(-1) s2.b.wls <- mse.w[1,1]*solve(t(X) %*% wm.wls %*% X) s.b.wls <- sqrt(diag(s2.b.wls)) # s{b_w} = sqrt(diag(s2{b_w})) t.b.wls <- b.wls/s.b.wls # t = b_w/s{b} p.b.wls <- 2*(1-pt(abs(t.b.wls), n-p)) # P-value

wls.out <- cbind(b.wls, s.b.wls, t.b.wls, p.b.wls) colnames(wls.out) <- c("b_wls", "Std. Error", "t*", "P(>|t*|)") rownames(wls.out) <- c("Intercept", "Height", "Arm Length", "Hand Length")

round(ols.out, 4) round(wls.out, 4)

###################################################################

## Using gls fuction in nlme package

library(nlme) gls.mod.ols <- gls(Weight ~ Height+ArmLng+HandLng, method="ML") summary(gls.mod.ols)

## Fit variance function model with s{e_i} = alpha*(mu_i^delta) gls.mod.wls <- gls(Weight ~ Height+ArmLng+HandLng, method="ML", weights=varPower(form = ~fitted(.))) summary(gls.mod.wls)

anova(gls.mod.ols,gls.mod.wls)

## Plot Pearson residuals (e/s{e}) vs yhat for OLS and WLS par(mfrow=c(1,2)) plot(resid(gls.mod.ols, type="p") ~ fitted(gls.mod.ols), pch=16, cex=0.6) abline(h=0, col="red") plot(resid(gls.mod.wls, type="p") ~ fitted(gls.mod.wls), pch=16, cex=0.6) abline(h=0, col="red")

par(mfrow=c(1,1))

NEED work sheet

Part 1: Ballistic Tests on various layers of cloth panels

p.1.a.

p.1.c.

p.1.d.

p.1.e.

p.1.f. Comment:

DATE

film	reissue	prodCost	usRev	forRev	totRev	profit	distCost	dC_tR	dC_pC	year	pctProf_totCost
STREET GIRL	0	211	806	198	1004	500	293	0.292	1.389	1930	99.2
VAGABOND LOVER	0	204	671	85	756	335	217	0.287	1.064	1930	79.6
SAINT IN NEW YO	0	128	350	310	460	195	137	0.298	1.07	1938	73.6
BACHELOR MOTHER	0	509	1170	805	1975	827	639	0.324	1.255	1939	72
TOP HAT	0	609	1782	1420	3202	1325	1268	0.396	2.082	1936	70.6
LITTLE WOMEN[*]	1	424	1337	663	2000	800	776	0.388	1.83	1934	66.7
RIO RITA	0	678	1775	625	2400	935	787	0.328	1.161	1930	63.8
CUCKOOS	0	407	662	201	863	335	121	0.14	0.297	1930	63.4
FIVE CAME BACK	0	225	441	280	721	265	231	0.32	1.027	1939	58.1
KITTY FOYLE	0	738	1710	675	2385	869	778	0.326	1.054	1941	57.3
MAN TO REMEMBER	0	118	293	123	416	146	152	0.365	1.288	1939	54.1
KING KONG[*]	1	672	745	1111	1856	650	534	0.288	0.795	1933	53.9
FOLLOW THE FLEE	0	747	1532	1175	2727	945	1035	0.38	1.386	1936	53
ANNE OF GREENIG	0	226	573	220	793	272	295	0.372	1.305	1935	52.2
INFORMER	0	243	455	495	950	325	382	0.402	1.572	1935	52
ROBERTA	0	610	1467	868	2335	770	955	0.409	1.566	1935	49.2
GAY DIVORCEE	0	520	1077	697	1774	584	670	0.378	1.288	1935	49.1
EX MRS BRADFORD	0	369	730	354	1084	350	365	0.337	0.989	1936	47.7
STAR OF MIDNIG[*]	1	280	575	256	831	265	286	0.344	1.021	1935	46.8
SKY GIANT	0	181	370	148	518	165	172	0.332	0.95	1938	46.7
SWING TIME	0	886	1624	994	2618	830	902	0.345	1.018	1936	46.4
FLYING DOWN TO	0	462	923	622	1545	480	603	0.39	1.305	1934	45.1
MELODY CRUISE	0	163	316	169	485	150	172	0.355	1.055	1933	44.8
CROSS FIRE	0	26	74	24	98	30	42	0.429	1.615	1933	44.1
SECOND WIFE	0	68	140	57	197	58	71	0.36	1.044	1936	41.7
HOOK LINE AND S	0	287	595	185	780	225	268	0.344	0.934	1931	40.5
COME ON DANGER	0	31	29	27	106	30	45	0.425	1.452	1933	39.5
PARTNERS	0	33	82	27	109	30	46	0.422	1.394	1932	38
MY FAVORITE WIF	0	921	1452	605	2057	505	631	0.307	0.685	1940	32.5
BRIDE WALKS OUT	0	289	502	168	670	164	217	0.324	0.751	1936	32.4
CRACKED NUTS	0	261	505	112	617	150	206	0.334	0.789	1931	32.1
GUN LAW[*]	1	78	148	47	195	47	70	0.359	0.897	1938	31.8
PHANTOM OF CRES	0	187	348	88	436	100	149	0.342	0.797	1933	29.8
FIFTH AVENUE GI	0	607	950	420	1370	314	449	0.328	0.74	1939	29.7
LUCKY DEVILS	0	117	179	106	285	65	103	0.361	0.88	1933	29.5
MARSHALL OF ME[*]	1	75	131	49	180	41	64	0.356	0.853	1940	29.5
IRENE	0	578	845	775	1620	367	675	0.417	1.168	1940	29.3
GRIDIRON FLASH	0	78	167	32	199	43	78	0.392	1	1935	27.6
SON OF KONG	0	269	331	285	616	133	214	0.347	0.796	1934	27.5
THAT'S RIGHT YO	0	271	926	92	1018	219	528	0.519	1.948	1940	27.4
ALICE ADAMS	0	342	574	196	770	164	264	0.343	0.772	1935	27.1
COMMON LAW	0	339	573	140	713	150	224	0.314	0.661	1932	26.6
BILL OF DIVORCE	0	250	383	148	531	110	171	0.322	0.684	1933	26.1
IN PERSON	0	493	496	219	715	147	75	0.105	0.152	1936	25.9
GHOST VALLEY	0	41	74	27	101	20	40	0.396	0.976	1932	24.7
MORNING GLORY	0	239	377	205	582	115	228	0.392	0.954	1934	24.6
SIX GUN GOLD	0	49	98	15	113	22	42	0.372	0.857	1941	24.2
SEVEN KEYS TO B	0	251	437	80	517	100	166	0.321	0.661	1930	24
SHALL WE DANCE	0	991	1275	893	2168	413	764	0.352	0.771	1937	23.5
LOVE COMES ALON	0	220	366	112	478	90	168	0.351	0.764	1930	23.2
SPITFIRE	0	223	492	112	604	113	268	0.444	1.202	1934	23
PACIFIC LINER	0	241	318	190	508	87	180	0.354	0.747	1939	20.7
MOST DANGEROUS	0	219	263	180	443	75	149	0.336	0.68	1933	20.4
SEA DEVILS	0	477	580	360	940	155	308	0.328	0.646	1937	19.7
CAUGHT PLASTERE	0	281	442	107	549	90	178	0.324	0.633	1932	19.6
YOU'LL FIND OUT	0	371	855	175	1030	167	492	0.478	1.326	1941	19.4
PEAGH O RENO	0	293	461	109	570	90	187	0.328	0.638	1932	18.8
MOTHER GAREY'S	0	358	543	160	703	110	235	0.334	0.656	1938	18.5
LOVING THE LADI	0	207	370	58	428	65	156	0.364	0.754	1930	17.9
LOST PATROL[*]	1	262	343	240	583	84	237	0.407	0.905	1934	16.8
LUGKY PARTNERS	0	733	880	510	1390	200	457	0.329	0.623	1940	16.8
TOM DIGK AND HA	0	806	1223	405	1628	234	588	0.361	0.73	1941	16.8
CHECK AND DOUBL	0	967	1751	59	1810	260	583	0.322	0.603	1931	16.8
DIPLOMANIACS	0	242	323	138	461	65	154	0.334	0.636	1933	16.4
BORN WITH LOVE	0	338	452	117	649	90	221	0.341	0.654	1932	16.1
YOU CAN'T BUY L	0	86	137	38	175	24	65	0.371	0.756	1937	15.9
LIFE OF VERGIE	0	331	506	148	654	87	236	0.361	0.713	1934	15.3
HIT THE DECK	0	542	980	152	1132	145	445	0.393	0.821	1930	14.7
EVERYTHING'S RO	0	140	205	70	275	35	100	0.364	0.714	1931	14.6
LOVE AFFAIR	0	860	975	775	1750	221	669	0.382	0.778	1939	14.5
MAD MISS MANTON	0	383	496	220	716	88	245	0.342	0.64	1939	14
IN NAME ONLY	0	722	926	395	1321	155	444	0.336	0.615	1939	13.3
ROOKIE COP	0	77	108	54	162	18	67	0.414	0.87	1939	12.5
THAT GIRL FROM	0	534	683	380	1063	101	428	0.403	0.801	1937	10.5
PRIMROSE PATH	0	702	898	302	1200	110	388	0.323	0.553	1940	10.1
DEVIL AND MISS	0	664	921	500	1421	117	640	0.45	0.964	1941	9
ANNIE OAKLEY	0	354	435	185	620	48	218	0.352	0.616	1936	8.4
RUNAWAY BRIDE	0	103	160	44	204	15	86	0.422	0.835	1930	7.9
SHOOTING STRAIG	0	238	378	40	418	30	150	0.359	0.63	1930	7.7
VIVACIOUS LADY[*]	1	703	830	376	1206	75	428	0.355	0.609	1937	6.6
THREE MUSKETEER	0	512	451	449	900	55	333	0.37	0.65	1935	6.5
GIRL A GUY AND	0	412	578	270	848	49	387	0.456	0.939	1941	6.1
MR AND MRS SMIT	0	743	981	419	1400	75	582	0.416	0.783	1941	5.7
STAGE DOOR	0	952	1250	512	1762	81	729	0.414	0.766	1938	4.8
HALF SHOT AT SU	0	529	658	271	929	40	360	0.388	0.681	1931	4.5
NURSE EDITH CAV	0	508	462	620	1082	38	536	0.495	1.055	1940	3.6
HUNGHBAGK OF NO	0	1826	1530	1625	3155	100	1229	0.39	0.673	1940	3.3
BREAK OF HEARTS	0	427	437	258	695	16	252	0.363	0.59	1935	2.4
DOUBLE HARNESS	0	329	379	114	493	10	154	0.312	0.468	1933	2.1
HIPS HIPS HOORA	0	336	435	190	625	8	281	0.45	0.836	1934	1.3
SUNNY	0	676	560	536	1096	7	413	0.377	0.611	1941	0.6
HE KNEW WOMEN	0	103	161	32	193	0	90	0.466	0.874	1930	0
NO NO NANETTE	0	570	490	450	940	-2	372	0.396	0.653	1941	-0.2
WINTER SET	0	407	467	215	682	-2	277	0.406	0.681	1937	-0.3
BACHELOR BAIT	0	120	168	27	19	-3	78	4.105	0.65	1934	-1.5
LITTLE MINSITER	0	648	723	381	1104	-9	465	0.421	0.718	1935	-0.8
GREAT MAN VOTES	0	265	337	95	432	-10	177	0.41	0.668	1939	-2.3
STORY OF V AND	0	1196	1120	705	1825	-50	679	0.372	0.568	1938	-2.7
MY LIFE WITH CA	0	503	530	300	830	-32	359	0.433	0.714	1941	-3.7
TRIPLE JUSTICE	0	85	110	19	129	-5	49	0.38	0.576	1940	-3.7
CAREFREE	0	1253	1113	618	1731	-68	546	0.315	0.436	1938	-3.8
BAD LANDS	0	84	108	33	141	-6	63	0.447	0.75	1939	-4.1
DAMSEL IN DISTR	0	1035	1010	455	1465	-65	495	0.338	0.478	1937	-4.2
SIN TAKES A HOL	0	450	463	160	623	-40	213	0.342	0.473	1931	-6
GUNGA DIN[*]	1	1915	1507	1300	2807	-193	1085	0.387	0.567	1939	-6.4
DEVOTION	0	394	448	94	542	-40	188	0.347	0.477	1932	-6.9
OF HUMAN BONDA[*]	1	403	467	125	592	-45	234	0.395	0.581	1934	-7.1
STINGAREE	0	408	368	195	563	-49	204	0.362	0.5	1934	-8
WHAT PRICE HOLL	0	616	430	141	571	-50	205	0.359	0.333	1932	-6.1
HOLD'EM JAIL	0	408	416	95	511	-55	158	0.309	0.387	1933	-9.7
MARY OF SCOTLAN	0	864	791	485	1276	-165	577	0.452	0.668	1936	-11.5
YOUNG DONAVON'S	0	279	445	173	618	-100	439	0.71	1.573	1931	-13.9
LOST SQUADRON[*]	1	621	534	198	732	-125	236	0.322	0.38	1932	-14.6
SILVER HORDE	0	423	418	144	562	-100	239	0.425	0.565	1931	-15.1
LIFE OF THE PAR	0	489	457	127	584	-111	206	0.353	0.421	1938	-16
SWISS FAMILY RO	0	681	587	303	890	-180	389	0.437	0.571	1940	-16.8
LIVING ON LOVE	0	112	106	29	135	-28	51	0.378	0.455	1938	-17.2
ANIMAL KINGDOM	0	458	439	89	528	-110	180	0.341	0.393	1933	-17.2
WISE GIRL	0	448	328	162	490	-114	156	0.318	0.348	1938	-18.9
LADY WITH A PAS	0	541	475	120	595	-140	194	0.326	0.359	1932	-19
LAST DAYS OF P[*]	1	818	489	491	980	-237	399	0.407	0.488	1935	-19.5
AFTER TONIGHT	0	355	250	130	380	-100	125	0.329	0.352	1933	-20.8
HAVING A WONDER	0	966	771	237	1008	-267	309	0.307	0.32	1938	-20.9
GIRL CRAZY	0	532	432	123	555	-150	173	0.312	0.325	1932	-21.3
QUICK MONEY	0	120	102	33	135	-37	52	0.385	0.433	1938	-21.5
JOY OF LIVING	0	1086	722	415	1137	-314	365	0.321	0.336	1938	-21.6
TOO MANY WIVES	0	105	92	30	122	-35	52	0.426	0.495	1937	-22.3
ALLEGHENY UPRIS	0	696	660	90	750	-230	284	0.379	0.408	1940	-23.5
THEY KNEW WHAT	0	781	577	355	932	-291	442	0.474	0.566	1941	-23.8
VIGIL IN THE NI	0	920	666	338	1004	-327	411	0.409	0.447	1940	-24.6
BRINGING UP THE BA[*]	1	1073	715	394	1109	-365	401	0.362	0.374	1937	-24.8
BIRD OF PARADIS	0	752	503	250	753	-250	251	0.333	0.334	1932	-24.9
NEW FAGES OF 1931	0	728	650	125	775	-258	305	0.394	0.419	1937	-25
WOMEN I LOVE	0	725	553	230	783	-266	324	0.414	0.447	1937	-25.4
CONSPIRACY	0	118	107	31	138	-50	70	0.507	0.593	1930	-26.6
GASE OF SGT GRI	0	467	407	49	456	-170	159	0.349	0.34	1930	-27.2
ROOM SERVIGE	0	884	665	210	875	-330	321	0.367	0.363	1939	-27.4
WOMAN REBELS	0	574	347	236	583	-222	231	0.396	0.402	1936	-27.6
DIXIANA	0	747	500	280	780	-300	333	0.427	0.446	1931	-27.8
RADIO CITY REV	0	810	565	185	750	-300	240	0.32	0.296	1938	-28.6
CIMARRON[*]	1	1433	1122	261	1383	-565	515	0.372	0.359	1931	-29
CONQUERORS	0	619	462	124	528	-230	139	0.263	0.225	1933	-30.3
TOAST OF NEW YO	0	1072	846	202	1048	-530	506	0.483	0.472	1937	-33.6
I DREAM TOO MUC	0	627	391	249	640	-350	363	0.567	0.579	1936	-35.4
HIS FAMILY TREE	0	127	89	27	116	-65	54	0.466	0.425	1936	-35.9
BEAU IDEAL	0	707	390	185	575	-330	198	0.344	0.28	1931	-36.5
MAN OF TWO WORL	0	388	194	114	308	-220	140	0.455	0.361	1934	-41.7
SILVIA SCARLET	0	641	321	176	497	-362	219	0.441	0.342	1936	-42.1
CAPTAIN HURRICA	0	208	124	26	150	-126	68	0.453	0.327	1935	-45.7
GAY DIPLOMAT	0	184	96	35	131	-115	62	0.473	0.337	1931	-46.7
HITTING A NEW H	0	727	305	183	488	-431	192	0.393	0.264	1938	-46.9
TWO ALONE	0	236	125	39	164	-158	86	0.524	0.364	1934	-49.1
WOMAN COMANDS	0	415	186	56	242	-265	92	0.38	0.222	1932	-52.3
ABE LINCOLN IN	0	1004	535	131	666	-740	402	0.604	0.4	1940	-52.6
ENCHANTED APRIL	0	346	127	38	165	-260	79	0.479	0.228	1935	-61.2