library("gdata")
## gdata: read.xls support for 'XLS' (Excel 97-2004) files ENABLED.
## 
## gdata: read.xls support for 'XLSX' (Excel 2007+) files ENABLED.
## 
## Attaching package: 'gdata'
## The following object is masked from 'package:stats':
## 
##     nobs
## The following object is masked from 'package:utils':
## 
##     object.size
ck = read.xls("/Users/ferarevalo1/Documents/Econometria 1 /CasoK.xls")
ck
##    Trimestre    CT    YT
## 1          1 192.5 202.3
## 2          2 196.1 197.1
## 3          3 196.9 202.9
## 4          4 197.0 202.2
## 5          5 198.1 203.5
## 6          6 199.0 211.7
## 7          7 199.4 215.3
## 8          8 200.6 215.1
## 9          9 199.9 212.9
## 10        10 203.6 213.9
## 11        11 204.8 214.0
## 12        12 209.0 214.9
## 13        13 210.7 228.0
## 14        14 214.2 227.3
## 15        15 225.6 232.0
## 16        16 217.0 236.1
## 17        17 222.3 230.9
## 18        18 214.5 236.3
## 19        19 217.5 239.1
## 20        20 219.8 240.8
## 21        21 220.0 238.1
## 22        22 222.7 240.9
## 23        23 223.8 245.8
## 24        24 230.2 248.8
## 25        25 234.0 253.3
## 26        26 236.2 256.1
## 27        27 236.0 255.9
## 28        28 234.1 255.9
## 29        29 233.4 254.4
## 30        30 236.4 254.8
## 31        31 239.0 257.0
## 32        32 243.2 260.9
## 33        33 248.7 263.0
## 34        34 253.7 271.5
## 35        35 259.9 276.5
## 36        36 261.8 281.4
## 37        37 263.2 282.0
## 38        38 263.7 286.2
## 39        39 263.4 287.7
## 40        40 266.9 291.0
## 41        41 268.9 291.1
## 42        42 270.4 294.6
## 43        43 273.4 296.1
## 44        44 272.1 293.3
## 45        45 268.9 291.3
## 46        46 270.9 292.6
## 47        47 274.4 299.9
## 48        48 278.7 302.1
## 49        49 283.8 305.9
## 50        50 289.7 312.5
## 51        51 290.8 311.3
## 52        52 292.8 313.2
## 53        53 295.4 315.4
## 54        54 299.5 320.3
## 55        55 298.6 321.0
## 56        56 299.6 320.1
## 57        57 297.0 318.4
## 58        58 301.6 324.8
library("lmtest")
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
reg1 = lm(formula = ck$CT ~ ck$YT, data = ck)
summary(reg1)
## 
## Call:
## lm(formula = ck$CT ~ ck$YT, data = ck)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0753 -2.8531 -0.5755  2.8859  9.0922 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.20030    3.37935   3.906 0.000255 ***
## ck$YT        0.88182    0.01279  68.935  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.719 on 56 degrees of freedom
## Multiple R-squared:  0.9884, Adjusted R-squared:  0.9881 
## F-statistic:  4752 on 1 and 56 DF,  p-value: < 2.2e-16
dwtest(reg1)
## 
##  Durbin-Watson test
## 
## data:  reg1
## DW = 1.1101, p-value = 9.213e-05
## alternative hypothesis: true autocorrelation is greater than 0
resid(reg1)
##           1           2           3           4           5           6 
##  0.90675637  9.09223996  4.77766211  5.49493875  5.44856785 -0.88238703 
##           7           8           9          10          11          12 
## -3.65695258 -2.28058783 -1.04057555  1.77760069  2.88941831  6.29577692 
##          13          14          15          16          17          18 
## -3.55611441  0.56116222  7.81659052 -4.39888692  5.48659667 -7.07525167 
##          19          20          21          22          23          24 
## -6.54435821 -5.74345862 -3.16253445 -2.93164099 -6.15257745 -2.39804874 
##          25          26          27          28          29          30 
## -2.56625569 -2.83536223 -2.85899748 -4.75899748 -4.13626183 -1.48899134 
##          31          32          33          34          35          36 
## -0.82900362 -0.06811631  3.58005378  1.08455177  2.87543294  0.45449649 
##          37          38          39          40          41          42 
##  1.32540223 -1.87825759 -3.50099324 -2.91101167 -0.99919404 -2.58557722 
##          43          44          45          46          47          48 
## -0.90831287  0.26079367 -1.17555880 -0.32192969 -3.25924318 -0.89925547 
##          49          50          51          52          53          54 
##  0.84981422  0.92977737  3.08796589  3.41250073  4.07248845  3.85155199 
##          55          56          57          58 
##  2.33427536  4.12791675  3.02701715  1.98334505
barplot(resid(reg1))

## Si hay autocorrelacion positiva

ck2 = read.xls("/Users/ferarevalo1/Documents/Econometria 1 /CasoK2.xls")
reg2 = lm(formula = ck2$Error ~ ck2$Errort)
summary(reg2)
## 
## Call:
## lm(formula = ck2$Error ~ ck2$Errort)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.5276 -1.6867  0.2818  2.0271  8.6741 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.01574    0.43782   0.036 0.971443    
## ck2$Errort   0.44420    0.12011   3.698 0.000496 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.334 on 56 degrees of freedom
## Multiple R-squared:  0.1963, Adjusted R-squared:  0.1819 
## F-statistic: 13.68 on 1 and 56 DF,  p-value: 0.0004961

El Ro tiene un coeficiente de 0.4420 lo que quiere decir que es significativo, creando una autocorrelacion positiva confirmando el metodo de Durwin Watson.