Loading Require Packages

library (dynlm)
## Warning: package 'dynlm' was built under R version 3.5.3
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.5.3
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

Data Preparation

  1. Download Example6_3.csv datasets

  2. Read Example6_3.csv data set into R Console

example6.3 <- read.csv (file.choose (), header = TRUE)

and choose Example6_3 data set in your downloaded folder.

Or, Copy and Paste the data set into your file directory and perform this code in R console.

example6.3 <- read.csv ("Example6_3.csv", header = TRUE)
  1. Since that we will works with time series data, it is best for us to define the data set as time series by using ts () function
example6.3 <- ts (example6.3, start = 1962, frequency = 1)
  1. Check the stucture of the dataset to ensure that R read our data set correctly.
str (example6.3) # check the structure
##  Time-Series [1:36, 1:9] from 1962 to 1997: 1962 1963 1964 1965 1966 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:9] "Year" "Cars" "UnemplRa" "GDP" ...
head (example6.3) # check the first 6 observations
##      Year Cars UnemplRa   GDP Export PopSize AvCarLan PerCapIn  CPI
## [1,] 1962 11.9      7.9 10426   2626     7.4      7.5     1409 31.3
## [2,] 1963 14.1      7.8 13077   2705     8.9      7.2     1469 32.2
## [3,] 1964 16.5      7.8 13932   2781     9.2      7.2     1514 32.1
## [4,] 1965 18.1      7.9 15400   3103     9.4      7.5     1638 32.9
## [5,] 1966 17.6      7.8 16376   3120     9.7      7.5     1688 33.4
## [6,] 1967 16.3      7.8 16612   3723    10.0      7.4     1661 34.8


List of all variables name

colnames (example6.3)
## [1] "Year"     "Cars"     "UnemplRa" "GDP"      "Export"   "PopSize"  "AvCarLan"
## [8] "PerCapIn" "CPI"
  1. Simple Plotting to check variables characteristics over time

    Plotting the variables except ‘Year’ variable
plot (example6.3[,-1], main = "Plotting for All Variables over Times (1962-1997)")

Comment: (Answer 1)

General-to-Specific Modelling

We will demonstrate on how to perform Model Estimation Procedure (General-to-Specific Approach) by using R Programming

Regression Model 1

reg1 <- dynlm(Cars~UnemplRa+GDP+Export+PopSize+AvCarLan+PerCapIn+CPI+L(Cars), data = example6.3)
summary (reg1)
## 
## Time series regression with "ts" data:
## Start = 1963, End = 1997
## 
## Call:
## dynlm(formula = Cars ~ UnemplRa + GDP + Export + PopSize + AvCarLan + 
##     PerCapIn + CPI + L(Cars), data = example6.3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -44.487  -7.154  -0.404   8.736  42.431 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -68.490721 120.329724  -0.569 0.574111    
## UnemplRa      6.041032   7.192849   0.840 0.408640    
## GDP          -0.005416   0.004463  -1.213 0.235877    
## Export        0.001423   0.001180   1.206 0.238688    
## PopSize      -2.310819  16.809494  -0.137 0.891718    
## AvCarLan     -5.795693   5.671624  -1.022 0.316255    
## PerCapIn      0.106478   0.057699   1.845 0.076396 .  
## CPI          -0.064020   1.438768  -0.044 0.964849    
## L(Cars)       0.932328   0.215747   4.321 0.000201 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.83 on 26 degrees of freedom
## Multiple R-squared:  0.963,  Adjusted R-squared:  0.9517 
## F-statistic: 84.67 on 8 and 26 DF,  p-value: < 2.2e-16

Comment: (Answer 2)

Regression Model 2

reg2 <- dynlm(Cars~UnemplRa+Export+PopSize+AvCarLan+PerCapIn+CPI+L(Cars), data = example6.3)
summary (reg2)
## 
## Time series regression with "ts" data:
## Start = 1963, End = 1997
## 
## Call:
## dynlm(formula = Cars ~ UnemplRa + Export + PopSize + AvCarLan + 
##     PerCapIn + CPI + L(Cars), data = example6.3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -40.352  -8.066   0.741   8.500  44.422 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.345e+01  5.198e+01   1.221 0.232760    
## UnemplRa     6.086e+00  7.255e+00   0.839 0.408962    
## Export       6.707e-05  3.822e-04   0.175 0.862023    
## PopSize     -1.615e+01  1.245e+01  -1.297 0.205589    
## AvCarLan    -6.531e+00  5.688e+00  -1.148 0.261001    
## PerCapIn     7.724e-02  5.288e-02   1.461 0.155663    
## CPI         -7.812e-01  1.323e+00  -0.590 0.559821    
## L(Cars)      8.779e-01  2.129e-01   4.124 0.000318 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.99 on 27 degrees of freedom
## Multiple R-squared:  0.9609, Adjusted R-squared:  0.9508 
## F-statistic: 94.89 on 7 and 27 DF,  p-value: < 2.2e-16

Comment: (Answer 3)

Regression Model 3

reg3 <- dynlm(Cars~UnemplRa+Export+AvCarLan+PerCapIn+CPI+L(Cars), data = example6.3)
summary (reg3)
## 
## Time series regression with "ts" data:
## Start = 1963, End = 1997
## 
## Call:
## dynlm(formula = Cars ~ UnemplRa + Export + AvCarLan + PerCapIn + 
##     CPI + L(Cars), data = example6.3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.216  -4.940  -0.819   8.499  53.431 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 47.5385857 51.1243344   0.930 0.360390    
## UnemplRa     0.1373883  5.6903397   0.024 0.980909    
## Export       0.0003430  0.0003214   1.067 0.294909    
## AvCarLan    -6.6973355  5.7557271  -1.164 0.254408    
## PerCapIn     0.0230321  0.0327941   0.702 0.488275    
## CPI         -0.9711533  1.3309798  -0.730 0.471663    
## L(Cars)      0.8708293  0.2153761   4.043 0.000374 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.22 on 28 degrees of freedom
## Multiple R-squared:  0.9585, Adjusted R-squared:  0.9496 
## F-statistic: 107.8 on 6 and 28 DF,  p-value: < 2.2e-16

Comment: (Answer 4)

Regression Model 4

reg4 <- dynlm(Cars~Export+AvCarLan+PerCapIn+CPI+L(Cars), data = example6.3)
summary (reg4)
## 
## Time series regression with "ts" data:
## Start = 1963, End = 1997
## 
## Call:
## dynlm(formula = Cars ~ Export + AvCarLan + PerCapIn + CPI + L(Cars), 
##     data = example6.3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.278  -4.893  -0.847   8.518  53.452 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 48.3930460 36.2537524   1.335    0.192    
## Export       0.0003476  0.0002544   1.366    0.182    
## AvCarLan    -6.6159001  4.5828373  -1.444    0.160    
## PerCapIn     0.0227653  0.0303402   0.750    0.459    
## CPI         -0.9679251  1.3012286  -0.744    0.463    
## L(Cars)      0.8670720  0.1463046   5.926 1.95e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.89 on 29 degrees of freedom
## Multiple R-squared:  0.9585, Adjusted R-squared:  0.9514 
## F-statistic:   134 on 5 and 29 DF,  p-value: < 2.2e-16

Comment: (Answer 5)

Regression Model 5

reg5 <- dynlm(Cars~Export+AvCarLan+CPI+L(Cars), data = example6.3)
summary (reg5)
## 
## Time series regression with "ts" data:
## Start = 1963, End = 1997
## 
## Call:
## dynlm(formula = Cars ~ Export + AvCarLan + CPI + L(Cars), data = example6.3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.970  -6.370   0.206   7.429  56.067 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 66.0337831 27.3952319   2.410  0.02227 *  
## Export       0.0004972  0.0001570   3.167  0.00353 ** 
## AvCarLan    -8.0146917  4.1559314  -1.928  0.06330 .  
## CPI         -0.0268940  0.3443225  -0.078  0.93826    
## L(Cars)      0.9015169  0.1379005   6.537 3.14e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.75 on 30 degrees of freedom
## Multiple R-squared:  0.9577, Adjusted R-squared:  0.9521 
## F-statistic: 169.8 on 4 and 30 DF,  p-value: < 2.2e-16

Comment: (Answer 6)

Regression Model 6

reg6 <- dynlm(Cars~Export+AvCarLan+L(Cars), data = example6.3)
summary (reg6)
## 
## Time series regression with "ts" data:
## Start = 1963, End = 1997
## 
## Call:
## dynlm(formula = Cars ~ Export + AvCarLan + L(Cars), data = example6.3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -40.084  -6.157   0.384   7.248  55.736 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 66.1549333 26.9092562   2.458 0.019741 *  
## Export       0.0004911  0.0001340   3.663 0.000922 ***
## AvCarLan    -8.1770225  3.5407782  -2.309 0.027751 *  
## L(Cars)      0.8998982  0.1341310   6.709 1.66e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.45 on 31 degrees of freedom
## Multiple R-squared:  0.9577, Adjusted R-squared:  0.9536 
## F-statistic: 233.9 on 3 and 31 DF,  p-value: < 2.2e-16

Comment: (Answer 7)