Gyakorló feladatok (Krasznahorkay Ilona oldaláról)

1. feladat. A feladatban a VH célváltozónak a többi (OZON, IBH, VIS, TEMP, DOY) változóktól való függését vizsgáltuk.
(a)  Adja meg a táblázatok hiányzó elemeit!
(b) Milyen eljárást futtattunk?
(c) Mi történik a második lépésben?
(d) Adja  meg a végső modellt, értelmezze a kapott paramétereket!
(e) Mit mondhatunk VH  értékéről, ha a magyarázó változók éppen az átlagos értéküket veszik fel?
(f) Mit tud mondani a hiba eloszlásáról?  (Minden rendelkezésre álló információ alapján döntsön!!!)

Regression

Descriptive Statistics

Mean Std. Deviation N
VH 5750,4848 105,70824 330
OZON 11,7758 8,01128 330
IBH 2572,8758 1803,88587 330
VIS 124,5333 79,36239 330
TEMP 61,7545 14,45874 330
DOY 181,7273 106,06059 330

Correlations

VH OZON IBH VIS TEMP DOY
Pearson Correlation VH 1,000 ,607 -,505 -,360 ,808 ,337
OZON ,607 1,000 -,590 -,441 ,781 ,066
IBH -,505 -,590 1,000 ,387 -,533 ,043
VIS -,360 -,441 ,387 1,000 -,388 -,217
TEMP ,808 ,781 -,533 -,388 1,000 ,238
DOY ,337 ,066 ,043 -,217 ,238 1,000
Sig. (1-tailed) VH , ,000 ,000 ,000 ,000 ,000
OZON ,000 , ,000 ,000 ,000 ,115
IBH ,000 ,000 , ,000 ,000 ,216
VIS ,000 ,000 ,000 , ,000 ,000
TEMP ,000 ,000 ,000 ,000 , ,000
DOY ,000 ,115 ,216 ,000 ,000 ,
N VH 330 330 330 330 330 330
OZON 330 330 330 330 330 330
IBH 330 330 330 330 330 330
VIS 330 330 330 330 330 330
TEMP 330 330 330 330 330 330
DOY 330 330 330 330 330 330

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 ??? , Forward (Criterion: Probability-of-F-to-enter <= ,050)
2 DOY , Forward (Criterion: Probability-of-F-to-enter <= ,050)
3 IBH , Forward (Criterion: Probability-of-F-to-enter <= ,050)
a Dependent Variable: VH

Model Summary(d)
Model R R Square Adjusted R Square Std. Error of the Estimate
1 ,808(a) ,653 ??? 62,36776
2 ,822(b) ??? ,673 60,42186
3 ???(c) ,690 ,687 59,12312
a Predictors: (Constant), TEMP
b Predictors: (Constant), TEMP, DOY
c Predictors: (Constant), TEMP, DOY, IBH
d Dependent Variable: VH

ANOVA(d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 2400488,437 1 2400488,437 ??? ,000(a)
Residual 1275833,988 328 3889,738

Total ??? 329


2 Regression 2482510,467 2 ??? 339,995 ,000(b)
Residual 1193811,957 327 ???

Total 3676322,424 329


3 Regression 2536775,157 ??? 845591,719 241,906 ,000(c)
Residual 1139547,267 ??? 3495,544

Total 3676322,424 329


a Predictors: (Constant), TEMP
b Predictors: (Constant), TEMP, DOY
c Predictors: (Constant), TEMP, DOY, IBH
d Dependent Variable: VH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B
Model B Std. Error Beta Lower Bound Upper Bound
1 (Constant) ??? 15,082
357,095 ,000 5355,986 5415,324
TEMP 5,908 ,238 ,808 24,842 ,000 5,440 6,376
2 (Constant) 5374,326 14,806
362,995 ,000 5345,200 5403,452
TEMP 5,640 ,237 ,771 ??? ,000 5,173 6,107
DOY ,153 ,032 ,154 4,740 ,000 ,090 ,217
3 (Constant) 5429,785 20,199
268,812 ,000 ??? ???
TEMP 5,023 ??? ,687 17,934 ,000 4,472 5,574
DOY ,180 ,032 ,180 5,555 ,000 ,116 ,243
IBH -8,598E-03 ,002 -,147 -3,940 ,000 -,013 -,004
a Dependent Variable: VH





Excluded Variables(d)

Beta In t Sig. Partial Correlation Collinearity Statistics
Model Tolerance
1 OZON -,060(a) -1,157 ,248 -,064 ,391
IBH -,104(a) -2,730 ,007 -,149 ,716
VIS -,055(a) -1,564 ,119 -,086 ,850
DOY ,154(a) 4,740 ,000 ,254 ,943
2 OZON -,014(b) -,265 ,791 -,015 ,375
IBH -,147(b) -3,940 ,000 -,213 ,686
VIS -,033(b) -,959 ,338 -,053 ,833
3 OZON -,080(c) -1,525 ,128 -,084 ,342
VIS ,003(c) ,079 ,937 ,004 ,773
a Predictors in the Model: (Constant), TEMP
b Predictors in the Model: (Constant), TEMP, DOY
c Predictors in the Model: (Constant), TEMP, DOY, IBH
d Dependent Variable: VH

Casewise Diagnostics(a)
Case Number Std. Residual VH
33 -3,815 5350,00
58 -3,445 5320,00
98 -3,015 5480,00
a Dependent Variable: VH

Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value 5523,6782 5935,4004 5750,4848 87,80981 330
Residual -225,5824 173,9485 ,0000 58,85295 330
Std. Predicted Value -2,583 2,106 ,000 1,000 330
Std. Residual -3,815 2,942 ,000 ,995 330
a Dependent Variable: VH

NPar Tests

One-Sample Kolmogorov-Smirnov Test

Unstandardized Residual
N 330
Normal Parameters(a,b) Mean -,0000001
Std. Deviation 58,85294724
Most Extreme Differences Absolute ,040
Positive ,040
Negative -,040
Kolmogorov-Smirnov Z ,728
Asymp. Sig. (2-tailed) ,663
a Test distribution is Normal.
b Calculated from data.

Graph

Histogram of res_1

PPlot 

MODEL:  MOD_1.

Expected Normal quantiles calculated using Blom's proportional
estimation formula and assigning the mean to ties.




For variable RES_1...

Normal distribution parameters estimated: location=,00000000 scale=58,852948

Normal p-p plot of unstandardized residual

2. feladat. A következő táblázat a nemzetgazdasági beruházások építésre fordított teljesítményértékét mutatja.
2002
 I.
 239,9

II.
 406,1

III.
 483,1

IV.
 811,2
2003.
 I.
 248,4

II.
 389,9

III.
 455,3

IV.
 884,4
2004.
 I.
 321,9

II.
 486,7

III.
 540,9

IV.
 901,6

(a) Illesszen lineáris trendet az idősorra! Értelmezze a főegyütthatókat!
(b) Adja meg a 2. és 3. negyedév nyers szezonális indexeit multiplikatív szezonalitást feltételezve!
(c) Adjon becslést a 2005. II. negyedévi adatokra!