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Econometrics

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Submitted By gulrot
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Del 1
A) Utfør en analyse av sammenhengen mellom vinens årgang (year) og prisen (målt ved prisindeksen).
Quick Estimate Equation
Alternativ 1: log(price) c t

Dependent Variable: LOG(PRICE) | | Method: Least Squares | | | Date: 05/03/11 Time: 10:25 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -1.074148 | 0.236263 | -4.546402 | 0.0001 | T | -0.023862 | 0.013049 | -1.828664 | 0.0785 | | | | | | | | | | | R-squared | 0.110203 | Mean dependent var | -1.455117 | Adjusted R-squared | 0.077248 | S.D. dependent var | 0.624716 | S.E. of regression | 0.600102 | Akaike info criterion | 1.883038 | Sum squared resid | 9.723306 | Schwarz criterion | 1.977334 | Log likelihood | -25.30405 | Hannan-Quinn criter. | 1.912570 | F-statistic | 3.344012 | Durbin-Watson stat | 2.469136 | Prob(F-statistic) | 0.078518 | | | | | | | | | | | | | |

| | | | | | | | | |
Signifikansnivået vurderes på bakgrunn av dette: “Alle forklaringsvariablene er signifikante fordi p-verdiene deres er mindre enn signifikansnivået på 5%”
Beholder hvis p-verdien er under signifikansnivået.
Alternativ 2: price c t

Dependent Variable: PRICE | | | Method: Least Squares | | | Date: 05/03/11 Time: 10:27 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | 0.418624 | 0.076877 | 5.445350 | 0.0000 | T | -0.008360 | 0.004246 | -1.969024 | 0.0593 | | | | | | | | | | | R-squared | 0.125564 | Mean dependent var | 0.285146 | Adjusted R-squared | 0.093178 | S.D. dependent var | 0.205053 | S.E. of regression | 0.195266 | Akaike info criterion | -0.362433 | Sum squared resid | 1.029481 | Schwarz criterion | -0.268136 | Log likelihood | 7.255271 | Hannan-Quinn criter. | -0.332900 | F-statistic | 3.877056 | Durbin-Watson stat | 2.503584 | Prob(F-statistic) | 0.059293 | | | | | | | | | | | | | |

Kovarians og Korrelasjon: Covariance Analysis: Ordinary | | Date: 05/04/11 Time: 08:40 | | Sample: 1952 1982 | | | Included observations: 29 | | Balanced sample (listwise missing value deletion) | | | | | | | | | Covariance | | | Correlation | YEAR | PRICE | T | YEAR | 72.92985 | | | | 1.000000 | | | | | | | PRICE | -0.609722 | 0.040597 | | | -0.354351 | 1.000000 | | | | | | T | 72.92985 | -0.609722 | 72.92985 | | 1.000000 | -0.354351 | 1.000000 | | | | | | | | |

Descriptive stats:

| H_RAIN | PRICE | T | TEMP | W_RAIN | YEAR | Mean | 145.2414 | 0.285146 | 15.96552 | 16.48104 | 606.1724 | 1966.966 | Median | 130.0000 | 0.221074 | 16.00000 | 16.41670 | 600.0000 | 1967.000 | Maximum | 292.0000 | 1.000000 | 31.00000 | 17.65000 | 830.0000 | 1982.000 | Minimum | 38.00000 | 0.101389 | 1.000000 | 14.98330 | 376.0000 | 1952.000 | Std. Dev. | 70.48741 | 0.205053 | 8.691058 | 0.677000 | 129.8142 | 8.691058 | Skewness | 0.612034 | 1.787856 | -0.018172 | -0.190256 | 0.027443 | -0.018172 | Kurtosis | 2.559761 | 6.396954 | 1.877457 | 2.353625 | 2.157495 | 1.877457 | | | | | | | | Jarque-Bera | 2.044685 | 29.39272 | 1.524221 | 0.679797 | 0.861333 | 1.524221 | Probability | 0.359751 | 0.000000 | 0.466680 | 0.711843 | 0.650076 | 0.466680 | | | | | | | | Sum | 4212.000 | 8.269238 | 463.0000 | 477.9501 | 17579.00 | 57042.00 | Sum Sq. Dev. | 139117.3 | 1.177309 | 2114.966 | 12.83320 | 471848.1 | 2114.966 | | | | | | | | Observations | 29 | 29 | 29 | 29 | 29 | 29 |
B) Estimer modell (1): log(price) c t h_rain w_rain temp og vurder hvilke varianler som har en significant effect på verdien av vin. Dependent Variable: LOG(PRICE) | | Method: Least Squares | | | Date: 05/03/11 Time: 08:25 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -11.86242 | 1.399617 | -8.475475 | 0.0000 | T | -0.022142 | 0.006095 | -3.633043 | 0.0013 | H_RAIN | -0.003788 | 0.000765 | -4.952749 | 0.0000 | W_RAIN | 0.001254 | 0.000427 | 2.937441 | 0.0072 | TEMP | 0.640194 | 0.078953 | 8.108531 | 0.0000 | | | | | | | | | | | R-squared | 0.832757 | Mean dependent var | -1.455117 | Adjusted R-squared | 0.804883 | S.D. dependent var | 0.624716 | S.E. of regression | 0.275950 | Akaike info criterion | 0.418392 | Sum squared resid | 1.827563 | Schwarz criterion | 0.654133 | Log likelihood | -1.066684 | Hannan-Quinn criter. | 0.492223 | F-statistic | 29.87585 | Durbin-Watson stat | 2.976373 | Prob(F-statistic) | 0.000000 | | | | | | | | | | | | | |

Signifikansnivået vurderes på bakgrunn av dette: “Alle forklaringsvariablene er signifikante fordi p-verdiene deres er mindre enn signifikansnivået på 5%”
“Alle verdiene har en signifikant effekt på pris fordi prob. Er mindre enn kristisk verdi. H_rain er stor, altså hvis det regner mye, så går prisen ned. Hvis H_rain øker med 1, så går prisen ned med 0,003788. Hvis tiden øker med 1 reduserer prisen tilsvarende med 0,022142.
Sum square resid er RSS
SD dependent var x n-1 = TSS
R-squared = R^2
Adjusted R-squared er justert R^2
F-statistic er f-verdien til hele modellen”

Heteroskedastisitet test
Må lage u-variabel- Quick generate series uvar=resid
Quick estimate equation: uvar^2 c t h_rain w_rain temp

Dependent Variable: UVAR^2 | | | Method: Least Squares | | | Date: 05/04/11 Time: 09:08 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | 10.08318 | 7.736415 | 1.303340 | 0.2073 | T | 0.006943 | 0.007021 | 0.988945 | 0.3345 | H_RAIN | 0.001462 | 0.001132 | 1.291119 | 0.2114 | W_RAIN | -0.001040 | 0.001113 | -0.934717 | 0.3611 | TEMP | -1.200551 | 0.956208 | -1.255534 | 0.2238 | T^2 | -0.000198 | 0.000216 | -0.914559 | 0.3713 | H_RAIN^2 | -3.90E-06 | 3.20E-06 | -1.217192 | 0.2377 | W_RAIN^2 | 9.27E-07 | 9.20E-07 | 1.007210 | 0.3259 | TEMP^2 | 0.036328 | 0.029198 | 1.244226 | 0.2278 | | | | | | | | | | | R-squared | 0.242128 | Mean dependent var | 0.063019 | Adjusted R-squared | -0.061021 | S.D. dependent var | 0.069917 | S.E. of regression | 0.072018 | Akaike info criterion | -2.174664 | Sum squared resid | 0.103733 | Schwarz criterion | -1.750331 | Log likelihood | 40.53263 | Hannan-Quinn criter. | -2.041768 | F-statistic | 0.798710 | Durbin-Watson stat | 2.008531 | Prob(F-statistic) | 0.610649 | | | | | | | | | | | | | |

Vi må finne frem til p-verdien??

View Residual diagnostics Hetero White huk av “include white cross terms”

Heteroskedasticity Test: White | | Heteroskedasticity Test: White | | | | | | | | | | | | F-statistic | 0.239710 | Prob. F(4,24) | 0.9130 | Obs*R-squared | 1.114090 | Prob. Chi-Square(4) | 0.8920 | Scaled explained SS | 1.889078 | Prob. Chi-Square(4) | 0.7562 | | | | | | | | | | | | | | | | Test Equation: | | | | Dependent Variable: RESID^2 | | | Method: Least Squares | | | Date: 05/04/11 Time: 09:31 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -0.012307 | 0.027225 | -0.452036 | 0.6553 | T^2 | 8.34E-07 | 7.27E-06 | 0.114648 | 0.9097 | H_RAIN^2 | 7.30E-09 | 8.62E-08 | 0.084645 | 0.9332 | W_RAIN^2 | -6.50E-09 | 1.33E-08 | -0.486729 | 0.6309 | TEMP^2 | 6.92E-05 | 9.32E-05 | 0.742473 | 0.4650 | | | | | | | | | | | R-squared | 0.038417 | Mean dependent var | 0.004494 | Adjusted R-squared | -0.121847 | S.D. dependent var | 0.010177 | S.E. of regression | 0.010780 | Akaike info criterion | -6.066721 | Sum squared resid | 0.002789 | Schwarz criterion | -5.830980 | Log likelihood | 92.96745 | Hannan-Quinn criter. | -5.992890 | F-statistic | 0.239710 | Durbin-Watson stat | 2.403867 | Prob(F-statistic) | 0.913047 | | | | | | | | | | | | | |

| | | | |

Heteroskedasticity Test: White | | | | | | | | | | | | F-statistic | 0.239710 | Prob. F(4,24) | 0.9130 | Obs*R-squared | 1.114090 | Prob. Chi-Square(4) | 0.8920 | Scaled explained SS | 1.889078 | Prob. Chi-Square(4) | 0.7562 | | | | | | | | | | | | | | | | Test Equation: | | | | Dependent Variable: RESID^2 | | | Method: Least Squares | | | Date: 05/04/11 Time: 09:31 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -0.012307 | 0.027225 | -0.452036 | 0.6553 | T^2 | 8.34E-07 | 7.27E-06 | 0.114648 | 0.9097 | H_RAIN^2 | 7.30E-09 | 8.62E-08 | 0.084645 | 0.9332 | W_RAIN^2 | -6.50E-09 | 1.33E-08 | -0.486729 | 0.6309 | TEMP^2 | 6.92E-05 | 9.32E-05 | 0.742473 | 0.4650 | | | | | | | | | | | R-squared | 0.038417 | Mean dependent var | 0.004494 | Adjusted R-squared | -0.121847 | S.D. dependent var | 0.010177 | S.E. of regression | 0.010780 | Akaike info criterion | -6.066721 | Sum squared resid | 0.002789 | Schwarz criterion | -5.830980 | Log likelihood | 92.96745 | Hannan-Quinn criter. | -5.992890 | F-statistic | 0.239710 | Durbin-Watson stat | 2.403867 | Prob(F-statistic) | 0.913047 | | | | | | | | | | | | | |

Test statistic: 24,14
Critical value: 15,5073 = F(8,20) s.526
24,14>15,5073
T-statistic er høyere enn kritisk verdi. Vi forkaster derfor nullhypotesen om homoskedastisitet. Vi har derfor påvist heteroskedastisitet.
H0: homo
HA: hetero (ikke homo)

Autokorrelasjon Estimer modell (1): log(price) c t h_rain w_rain temp
View residual diagnostics serial correlation LM test lags to include: 1

Breusch-Godfrey Serial Correlation LM Test: | | | | | | | | | | | | F-statistic | 5.347712 | Prob. F(1,23) | 0.0300 | Obs*R-squared | 5.470764 | Prob. Chi-Square(1) | 0.0193 | | | | | | | | | | | | | | | | Test Equation: | | | | Dependent Variable: RESID | | | Method: Least Squares | | | Date: 05/03/11 Time: 09:16 | | | Sample: 1952 1982 | | | Included observations: 29 | | | Presample and interior missing value lagged residuals set to zero. | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -0.256503 | 1.292589 | -0.198441 | 0.8444 | T | 0.000855 | 0.005620 | 0.152212 | 0.8803 | H_RAIN | 6.72E-05 | 0.000704 | 0.095423 | 0.9248 | W_RAIN | -2.08E-05 | 0.000393 | -0.052883 | 0.9583 | TEMP | 0.014808 | 0.072928 | 0.203052 | 0.8409 | RESID(-1) | -0.446703 | 0.193168 | -2.312512 | 0.0300 | | | | | | | | | | | R-squared | 0.188647 | Mean dependent var | 2.07E-15 | Adjusted R-squared | 0.012266 | S.D. dependent var | 0.255480 | S.E. of regression | 0.253908 | Akaike info criterion | 0.278305 | Sum squared resid | 1.482798 | Schwarz criterion | 0.561194 | Log likelihood | 1.964571 | Hannan-Quinn criter. | 0.366903 | F-statistic | 1.069542 | Durbin-Watson stat | 2.387057 | Prob(F-statistic) | 0.402742 | | | |

RESET-Test
Estimate equation: log(price) c t h_rain w_rain temp (log(price))^2 (log(price))^3
Estimert før Ramsey-testen:

Dependent Variable: LOG(PRICE) | | Method: Least Squares | | | Date: 05/03/11 Time: 10:02 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -1.478190 | 0.624523 | -2.366910 | 0.0272 | T | -0.002727 | 0.001745 | -1.563245 | 0.1323 | H_RAIN | -0.000473 | 0.000257 | -1.836374 | 0.0799 | W_RAIN | 0.000170 | 0.000117 | 1.461607 | 0.1580 | TEMP | 0.067966 | 0.035214 | 1.930052 | 0.0666 | (LOG(PRICE))^2 | -0.843031 | 0.060455 | -13.94486 | 0.0000 | (LOG(PRICE))^3 | -0.219291 | 0.023189 | -9.456831 | 0.0000 | | | | | | | | | | | R-squared | 0.991327 | Mean dependent var | -1.455117 | Adjusted R-squared | 0.988962 | S.D. dependent var | 0.624716 | S.E. of regression | 0.065634 | Akaike info criterion | -2.402946 | Sum squared resid | 0.094772 | Schwarz criterion | -2.072909 | Log likelihood | 41.84271 | Hannan-Quinn criter. | -2.299582 | F-statistic | 419.1153 | Durbin-Watson stat | 2.380589 | Prob(F-statistic) | 0.000000 | | | | | | | | | | | | | |

View stability RESET: L= 2 = number of new regressors

Ramsey RESET Test | | | Equation: UNTITLED | | | Specification: LOG(PRICE) C T H_RAIN W_RAIN TEMP (LOG(PRICE))^2 | (LOG(PRICE))^3 | | | Omitted Variables: Powers of fitted values from 2 to 3 | | | | | | | | | | | | Value | df | Probability | | F-statistic | 80.62038 | (2, 20) | 0.0000 | | Likelihood ratio | 63.91873 | 2 | 0.0000 | | | | | | | | | | | | F-test summary: | | | | Sum of Sq. | df | Mean Squares | | Test SSR | 0.084313 | 2 | 0.042157 | | Restricted SSR | 0.094772 | 22 | 0.004308 | | Unrestricted SSR | 0.010458 | 20 | 0.000523 | | Unrestricted SSR | 0.010458 | 20 | 0.000523 | | | | | | | | | | | | LR test summary: | | | | Value | df | | | Restricted LogL | 41.84271 | 22 | | | Unrestricted LogL | 73.80208 | 20 | | | | | | | | | | | | | | | | | | Unrestricted Test Equation: | | | Dependent Variable: LOG(PRICE) | | Method: Least Squares | | | Date: 05/03/11 Time: 09:56 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -2.210842 | 0.247671 | -8.926544 | 0.0000 | T | -0.003638 | 0.000626 | -5.810897 | 0.0000 | H_RAIN | -0.000770 | 9.79E-05 | -7.864258 | 0.0000 | W_RAIN | 0.000278 | 4.33E-05 | 6.406876 | 0.0000 | TEMP | 0.112545 | 0.013964 | 8.059814 | 0.0000 | (LOG(PRICE))^2 | -1.963098 | 0.152515 | -12.87147 | 0.0000 | (LOG(PRICE))^3 | -0.473442 | 0.058427 | -8.103083 | 0.0000 | FITTED^2 | 1.064452 | 0.152531 | 6.978574 | 0.0000 | FITTED^3 | 0.225067 | 0.060389 | 3.726955 | 0.0013 | | | | | | | | | | | R-squared | 0.999043 | Mean dependent var | -1.455117 | Adjusted R-squared | 0.998660 | S.D. dependent var | 0.624716 | S.E. of regression | 0.022867 | Akaike info criterion | -4.469109 | Sum squared resid | 0.010458 | Schwarz criterion | -4.044776 | Log likelihood | 73.80208 | Hannan-Quinn criter. | -4.336213 | F-statistic | 2609.727 | Durbin-Watson stat | 1.781623 | Prob(F-statistic) | 0.000000 | | | | | | | | | | | | | |

Vi tester om de er signifikante ved hjelp av en F-test.
F=( (R^2new – R^2old)/L ) / ((1-R^2new)(n-numbers of parameters in the new model))
F=( (0,999043-0,991327)/2 ) / ((1- 0,999043)/(29-6)) = 0.0039/0.0000416087 = 93.731974

Kristisk Verdi 5% signifikansnivå: F(q=6,n-q-1=29-6-1=22) = 2,55

F (93,73) > Kritisk verdi (2,55)

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