List of Tables and Figures

Contents Page No.

Table 1.1: OLS Estimates of Imports, Gross Domestic Product & Consumer Price Index - 02
Table 1.2: OLS Estimates of Three Models ------------------------------------------------------- 04
Table 2.1: OLS Estimates of Imports, Gross Domestic Product & Consumer Price Index - 07
Table 2.2: OLS Estimates of Three Models------------------------------------------------------- 08
Table 3.1: OLS Estimates of Price, Lot-size, Square-feet, and Bedrooms -------------------- 11
Table 3.2: Heteroskedasticity Test: Breusch-Pagan-Godfrey ----------------------------------- 12
Table 3.3: Comparison of OLS Estimates and Re-esimated Estimates ------------------------ 13
Table 3.4: Comparison of OLS Estimates and Log(Price) Model ------------------------------ 14
Table 4.1: OLS Estimates of Investment, Income and Interest rate ---------------------------- 16
Table 4.2: Autocorrelation --------------------------------------------------------------------------- 17

Figure 3.1: Graph of Heteroskedasticity ----------------------------------------------------------- 12

Figure 3.2: Graph of Heteroskedasticity for Log(Price) Model -------------------------------- 15
Figure 4.1: Graph of Residuals ---------------------------------------------------------------------- 17
 Assignment # 4

Question No 1:The file imports_UK.xls contains quarterly data for imports (imp), gross

domestic product (gdp) and the consumer price index (cpi) for the UK.

a. Use these data to estimate the following model. Ln (imp)t =β1+β2+ln(gdp)t+β3ln(cpi)t+εt

and Check whether there is multicollinearity in the data . Calculate the correlation matrix

of the variables and comment regarding the possibility of the multicollinearity.

Table 1.1: OLS Estimates of Imports, Gross Domestic Product & Consumer Price Index
Pair wise Correlation Estimates Variance Inflation Factor
Coefficient Centered
Imports GDP CPI Variable Coefficient
Variance VIF
0.506395*
Imports
(0.295304)
1 Constant 0.087204 NA
[1.714828]

2.136145***
0.987682 (0.105433)
GDP 1 GDP 0.011116 3.95912
*** [20.26059]

0.107142**
0.878005 0.864534
CPI 1 CPI (0.050123) 0.002512 3.95912
*** ***
[2.137587]
Statistical Measures
R-squared 0.97782 Adjusted R-squared 0.976812
F-statistic 969.8746 Prob(F-statistic) 0.000
Dependent Variable; Imports
Independent Variable; Gross Domestic Product (GDP)
Consumer Price Index (CPI)
Constant: C
*** Sig. at 1%, ** Sig. at 5%, * Sig. at 10%, ( ) = Standard Error, [ ] = t-statistics

Interpretation:

 Table 1.1 shows that if GDP and CPI are zero than still there are 0.506395 units of
imports. t-calculated (1.714828) is greater than t-critical (1.645), and p-value (0.0934) is
less than 10 %, so coefficient of constant is significant at 10%.

2
 Assignment # 4

 One percent increase in GDP increases 2.136145 percent of imports assuming that CPI is
constant. t-calculated (20.26059) is greater than t-critical (1.645), and p-value (0.000) is
greater than 10 %, so The coefficient of GDP is significant at 1%, this leads to acceptance
of H1.
 One percent increase in CPI increases 0.107142 percent of imports assuming that GDP is
constant. t-calculated (2.137587) is greater than t-critical (1.645), and p-value (0.0381) is
less than 10 %, so The coefficient of CPI is significant at 5%, this leads to acceptance of
H2.
 Estimated model will be;

Ln (imp)t =β1+β2ln(gdp)t+β3ln(cpi)t+εt
Ln (imp)t = 0.506395+ 2.136145 ln(gdp)t+0.107142 ln(cpi)t+εt

 Adjusted R-squared explains that 97.6812% variation in imports is explained by GDP

and CPI.
 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 If VIF is greater than 10% this means there is multicollinearilty. Table 1.1 shows that
VIF is less than 10 %, so there is no multicollinearity.
 Pair wise correlation suggests that there is strong correlation among variables.
 One method to detect multicollinearity is “High pair-wise correlation among regressors”.
Results of pair-wise correlation suggest that there is high pair-wise correlation (> 0.8),
that is indication of multicollinearity, but it is not necessary there will be multicollinearity
when there will be high pair-wise correlation among regressors.

b. Also run the following additional regressions:

Ln(imp)t=β1+β2ln(gdp)t+εt

Ln(imp)t=β1+β2ln(cpi)t+εt

Ln(gdp)t=β1+β2ln(cpi)t+εt

What can you conduct about the nature of multicollinearity from these results?

3
 Assignment # 4

Table 1.2: OLS Estimates of Three Models

Estimates

Model 1 Model 2 Model 3

Variables
Ln(imp)t=β1+β2ln(gdp)t+εt Ln(imp)t=β1+β2ln(cpi)t+εt Ln(gdp)t=β1+β2ln(cpi)t+εt

1.188584*** 5.942083*** 2.544625***

Constant (0.126015) (0.392142) (0.174462)
[9.432117] [15.15288] [14.58552]
2.102296***
GDP (0.028212)
[74.51882]
0.985095*** 0.410999***
CPI (0.080056) (0.035617)
[12.30506] [11.53951]
Statistical Measures
R-
0.987025 0.770893 0.747419
Squared
Adjusted
R- 0.986847 0.765801 0.741806
Squared
F-statistic 5553.055 151.4145 133.1604
Prob(F-
0.000 0.000 0.000
statistic)
Variance Inflation Factor
Coefficient Centered Coefficient Centered Coefficient Centered
Variance VIF Variance VIF Variance VIF
Constant 0.01588 NA 0.153775 NA 0.030437 NA
GDP 0.000796 1
CPI 0.006409 1 0.001269 1
Dependent Variable; Imports {In model 3 GDP is took as dependent variable}
Independent Variable; Gross Domestic Product (GDP)
Consumer Price Index (CPI)
Constant: C

*** Sig. at 1%, ** Sig. at 5%, * Sig. at 10%, ( ) = Standard Error, [ ] = t-statistics

4
 Assignment # 4

Interpretation:
Model 1:

 Table 1.2 shows that if GDP is zero than still there are 1.188584 units of imports. t-
calculated (9.432117) is greater than t-critical (1.645), and p-value (0.000) is less than 10
%, so coefficient of constant is significant at 1%.
 One percent increase in GDP increases 0.410999 percent of imports. t-calculated
(74.51882) is greater than t-critical (1.645), and p-value (0.000) is greater than 10 %, so
The coefficient of GDP is significant at 1%, this leads to acceptance of H1.
 Estimated model will be;

Ln (imp)t =β1+β2ln(gdp)t+ εt
Ln (imp)t = 1.188584 + 2.102296 ln(gdp)t +εt

 R-squared explains that 98.7025% variation in imports is explained by GDP.

 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 1.2 shows that VIF is less than 10 %, so there is no multicollinearity.

Model 2:

 Table 1.2 shows that if CPI is zero than still there are 5.942083 units of imports. t-
calculated (15.15288) is greater than t-critical (1.645), and p-value (0.000) is less than 10
%, so coefficient of constant is significant at 1%.
 One percent increase in CPI increases 0.985095 percent of imports. t-calculated
(12.30506) is greater than t-critical (1.645), and p-value (0.000) is less than 10 %, so The
coefficient of CPI is significant at 1%, this leads to acceptance of H2.
 Estimated model will be;

Ln (imp)t =β1+β2ln(cpi)t+εt
Ln (imp)t = 5.942083+0.985095 ln(cpi)t+εt

 R-squared explains that 77.0893% variation in imports is explained by CPI.

 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 1.2 shows that VIF is less than 10 %, so there is no multicollinearity.

5
 Assignment # 4

Model 3:

 Table 1.2 shows that if CPI is zero than still there are 2.544625 units of GDP. t-calculated
(14.58552) is greater than t-critical (1.645), and p-value (0.000) is less than 10 %, so
coefficient of constant is significant at 1%.
 One percent increase in CPI increases 0.410999 percent of imports. t-calculated
(11.53951) is greater than t-critical (1.645), and p-value (0.000) is less than 10 %, so The
coefficient of CPI is significant at 1%, this leads to acceptance of H3.
 Estimated model will be;

Ln (imp)t =β1+β2ln(cpi)t+εt
Ln (imp)t = 2.544625 +0.410999 ln(cpi)t+εt

 R-squared explains that 74.7419% variation in GDP is explained by CPI.

 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 1.2 shows that VIF is less than 10 %, so there is no multicollinearity.

______________________________________________________________________________

Question No 2: The file import_UK_Y.xls contains observations of the variables mentioned in

question 1.Repeat exercise in question 1 using yearly data .Do your results change?

Interpretation:

 Table 2.1 (on next page) shows that if GDP and CPI are zero than still there are 2.503281
units of imports. t-calculated (8.392276) is greater than t-critical (1.645), and p-value
(0.0934) is less than 10 %, so coefficient of constant is significant at 10%.
 One percent increase in GDP increases 2.158164 percent of imports assuming that CPI is
constant. t-calculated (23.29457) is greater than t-critical (1.645), and p-value (0.000) is
greater than 10 %, so The coefficient of GDP is significant at 1%, this leads to acceptance
of H1.

6
 Assignment # 4

Table 2.1: OLS Estimates of Imports, Gross Domestic Product & Consumer Price Index
Pair wise Correlation Estimates Variance Inflation Factor
Coefficient Centered
Imports GDP CPI Variable Coefficient
Variance VIF
2.503281***
Imports
(0.298284)
1 Constant 0.088973 NA
[8.392276]

2.158164***
0.996014 (0.092647)
GDP 1 GDP 0.008583 5.870875
*** [23.29457]

-0.04174
0.896672 0.910861
CPI 1 CPI (0.030425) 0.000926 5.870875
*** ***
[-1.37192]
Statistical Measures
R-squared 0.992698 Adjusted R-squared 0.992003
F-statistic 1427.503 Prob(F-statistic) 0.000
Dependent Variable; Imports
Independent Variable; Gross Domestic Product (GDP)
Consumer Price Index (CPI)
Constant: C
*** Sig. at 1%, ** Sig. at 5%, * Sig. at 10%, ( ) = Standard Error, [ ] = t-statistics

 One percent increase in CPI decreases 0.04174 percent of imports assuming that GDP is
constant. t-calculated (1.37192) is less than t-critical (1.645), and p-value (0.1846) is
greater than 10 %, so The coefficient of CPI is insignificant at 10%, this leads to rejection
of H2.
 Adjusted R-squared explains that 99.2698% variation in imports is explained by GDP
and CPI.
 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 2.1 shows that VIF is less than 10 %, so there is no multicollinearity.
 Pair wise correlation suggests that there is strong correlation among variables.
 Results of pair-wise correlation suggest that there is high pair-wise correlation (> 0.8),
which is indication of multicollinearity.

7
 Assignment # 4

Table 2.2: OLS Estimates of Three Models

Estimates
Model 1 Model 2 Model 3
Variables
Ln(imp)t=β1+β2ln(gdp)t+εt Ln(imp)t=β1+β2ln(cpi)t+εt Ln(gdp)t=β1+β2ln(cpi)t+εt

2.841244*** 9.346217*** 3.170721***

Constant (0.17153) (0.262046) (0.119137)
[16.5641] [35.66637] [26.61403]
2.04239***
GDP (0.038996)
[52.37488]
0.603811*** 0.29912***
CPI (0.063557) (0.028896)
[9.500364] [10.35178]
Statistical Measures
R-
0.992044 0.804021 0.829668
Squared
Adjusted
R- 0.991682 0.795113 0.821925
Squared
F-statistic 2743.128 90.25691 107.1593
Prob(F-
0.000 0.000 0.000
statistic)
Variance Inflation Factor
Coefficient Centered Coefficient Centered Coefficient Centered
Variance VIF Variance VIF Variance VIF
Constant 0.029423 NA 0.068668 NA 0.014194 NA
GDP 0.001521 1
CPI 0.004039 1 0.000835 1
Dependent Variable; Imports {In model 3 GDP is took as dependent variable}
Independent Variable; Gross Domestic Product (GDP)
Consumer Price Index (CPI)
Constant: C
*** Sig. at 1%, ** Sig. at 5%, * Sig. at 10%, ( ) = Standard Error, [ ] = t-statistics

8
 Assignment # 4

Interpretation:
Model 1:

 Table 2.2 shows that if GDP is zero than still there are 2.841244 units of imports. t-
calculated (16.5641) is greater than t-critical (1.645), and p-value (0.000) is less than 10
%, so coefficient of constant is significant at 1%.
 One percent increase in GDP increases 2.04239 percent of imports. t-calculated
(52.37488) is greater than t-critical (1.645), and p-value (0.000) is greater than 10 %, so
The coefficient of GDP is significant at 1%, this leads to acceptance of H1.
 Estimated model will be;

Ln (imp)t =β1+β2ln(gdp)t+ εt
Ln (imp)t = 2.841244 + 2.04239 ln(gdp)t +εt

 R-squared explains that 99.2044% variation in imports is explained by GDP.

 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 2.2 shows that VIF is less than 10 %, so there is no multicollinearity.

Model 2:

 Table 2.2 shows that if CPI is zero than still there are 9.346217 units of imports. t-
calculated (35.66637) is greater than t-critical (1.645), and p-value (0.000) is less than 10
%, so coefficient of constant is significant at 1%.
 One percent increase in CPI increases 0.603811 percent of imports. t-calculated
(9.500364) is greater than t-critical (1.645), and p-value (0.000) is less than 10 %, so The
coefficient of CPI is significant at 1%, this leads to acceptance of H2.
 Estimated model will be;

Ln (imp)t =β1+β2ln(cpi)t+εt
Ln (imp)t = 9.346217 +0.603811 ln(cpi)t+εt

 R-squared explains that 80.4021% variation in imports is explained by CPI.

 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 2.2 shows that VIF is less than 10 %, so there is no multicollinearity.

9
 Assignment # 4

Model 3:

 Table 2.2 shows that if CPI is zero than still there are 3.170721 units of GDP. t-calculated
(26.61403) is greater than t-critical (1.645), and p-value (0.000) is less than 10 %, so
coefficient of constant is significant at 1%.
 One percent increase in CPI increases 0.29912 percent of imports. t-calculated
(10.35178) is greater than t-critical (1.645), and p-value (0.000) is less than 10 %, so The
coefficient of CPI is significant at 1%, this leads to acceptance of H3.
 Estimated model will be;

Ln (imp)t =β1+β2ln(cpi)t+εt
Ln (imp)t = 3.170721 +0.29912 ln(cpi)t+εt

 R-squared explains that 82.9668 % variation in GDP is explained by CPI.

 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.
 Table 2.2 shows that VIF is less than 10 %, so there is no multicollinearity.

Comparison with Question 1:

 Adjusted R-Square for multiple regressions is higher in question 2 as compared to

question 1.

 R-squared for simple regression of all three models in question 1 is also higher than

question 1.

 Intercept in question 2 of multiple regressions and simple regression model is greater

than models of question 1.

 Slope of all simple regression models in question 2 is lesser than models of question 1.

Slope of GDP in multiples regression model of question 2 is slightly higher than of

question 1. While CPI have positive slope in question 1 and negative slope in question 2.

 There is slightly less multicollinearity as compared to question 1.

 All models are good fit.

10
 Assignment # 4

 Pair-wise correlation among variables in question 2 is slight higher than question 1.

______________________________________________________________________________

Question No 3: Use the data in the file houseprice.xls to estimate the following equation:

Price= α0+α1lotsize+α2sqfeet+α3bdrms+ε

Table 3.1: OLS Estimates of Price, Lot-size, Square-feet, and Bedrooms

Estimates
Variable Coefficient Std. Error t-Statistic Prob.
C -21770.3 29475.04 -0.7386 0.4622
LOTSIZE 2.067707 0.642126 3.220096 0.0018
SQRFT 122.7782 13.23741 9.275093 0.000
BDRMS 13852.52 9010.145 1.537436 0.1279
Statistical Measures
R-squared 0.672362 Adjusted R-squared 0.660661
F-statistic 57.46023 Prob (F-statistic) 0.000
Dependent Variable; Price
Independent Variable; Lot-size, Square-feet, Bedrooms
Constant: C

 Table 3.1 shows that if lot-size, square-feet and bedrooms are zero than still there are -
21770.3 units of price. t-calculated (0.7386) is less than t-critical (1.645), and p-value
(0.4622) is greater than 10 %, so coefficient of constant is insignificant at 10%.
 One unit increase in lot-size increases 2.067707 units of price assuming that square-feet
and bedrooms are constant. t-calculated (3.220096) is greater than t-critical (1.645), and
p-value (0.0018) is greater than 10 %, so The coefficient of lot-size is significant at 5%,
this leads to acceptance of H1.
 One unit increase in square-feet increases 122.7782 units of price assuming that lot-size
and bedrooms are constant. t-calculated (9.275093) is greater than t-critical (1.645), and
p-value (0.000) is less than 10 %, so The coefficient of square-feet is significant at 5%,
this leads to acceptance of H2.
 One unit increase in bedrooms increases 13852.52 units of price assuming that lot-size
and square-feet are constant. t-calculated (1.537436) is less than t-critical (1.645), and p-

11
 Assignment # 4

value (0.1279) is greater than 10 %, so The coefficient of bedrooms is insignificant at

10%, this leads to rejection of H3.
 Adjusted R-squared explains that 66.0661% variation in price is explained by lot-size,
square-feet and bedrooms.
 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.

a.) Check whether there is evidence of Heteroskedasticity using formal and informal methods.

Informal Method:

There is no certain pattern followed in graph. There are some highest peaks and some are lowest.
This shows that there is heteroskedasticity in data.
GENRUTSQ
5E+10

4E+10

3E+10

2E+10

1E+10

0E+00
10 20 30 40 50 60 70 80

Figure 3.1: Graph of Heteroskedasticity

Formal Method:
Heteroskedasticity Test: Breusch-Pagan-Godfrey

Table 3.2: Heteroskedasticity Test: Breusch-Pagan-Godfrey

Null Hypothesis: there is homoskedasticity
F-statistic 5.338919 Prob. F(3,84) 0.002
Obs*R-squared 14.09239 Prob. Chi-Square(3) 0.0028
Scaled explained SS 27.35542 Prob. Chi-Square(3) 0.000

12
 Assignment # 4

Table 3.2 shows that probability of Chi-square is less 10 % so we reject null hypothesis. This
demonstrates that heteroskedasticity exist in data.

b.) Reestimate the model correcting for Heteroskedasticity using white Heteroskedasticity
standard errors and compare the results obtained through simple OLS

Table 3.3: Comparison of OLS Estimates and Re-esimated Estimates

Estimates
OLS Reestimated
Variable Estimates Estimates Comparison
-21770.3 -21770.3
C (29475.04) (37138.21) Intercept is same
[-0.7386] [-0.5862]
2.067707** 2.067707 Slope of lotsize is same
LOTSIZE (0.642126) (1.251424) but coefficient become
[3.220096] [1.652283] insignificant.
122.7782*** 122.7782***
SQRFT (13.23741) (17.72533) Slope of Sqfrt is same.
[9.275093] [6.926707]
13852.52 13852.52
BDRMS (9010.145) (8478.625) Slope of Sqfrt is same
[1.537436] [1.633817]
Statistical Measures
R-squared 0.672362 0.672362
Adjusted R-squared 0.660661 0.660661
All results are same.
F-statistic 57.46023 57.46023
Prob (F-statistic) 0.000 0.000
Dependent Variable; Price
Independent Variable; Lot-size, Square-feet, Bedrooms
Constant: C
*** Sig. at 1%, ** Sig. at 5%, * Sig. at 10%, ( ) = Standard Error, [ ] = t-statistics

c.) Reestimate the equation but this time instead of price use log(price) as the dependent variable.
Check for Heteroskedasticity again. Is there any change in your conclusion in (a)

13
 Assignment # 4

Table 3.4: Comparison of OLS Estimates and Log(Price) Model

Estimates
OLS Estimates
OLS
Variable Log(Price) Comparison
Estimates
Model
-21770.3 11.66713***
Intercept of log model
C (29475.04) (0.093536)
is significant
[-0.7386] [124.734]
2.067707** 5.60E-06***
Slope of lotsize
LOTSIZE (0.642126) (2.04E-06
increased..
[3.220096] [2.749042])
122.7782*** 0.000364***
Slope of Sqfrt
SQRFT (13.23741) (4.20E-05
decreased.
[9.275093] [8.667894])
13852.52 0.025239
Slope of Sqfrt also
BDRMS (9010.145) (0.028593)
decreased.
[1.537436] [0.882698]
Statistical Measures
R-squared 0.672362 0.622277 Decreased
Adjusted R-squared 0.660661 0.608787 Decreased
F-statistic 57.46023 46.12847 Decreased
Prob (F-statistic) 0.000 0.000 Same
Heteroskedasticity Test: Breusch-Pagan-Godfrey
Null Hypothesis: there is homoskedasticity
F-statistic 5.338919 1.174494 Simple model data is
Obs*R-squared 14.09239 3.542665 heteroskedasticity and
Scaled explained SS 27.35542 7.960963 log model is
Prob. F(3,84) 0.002 0.3244 homoskedastic on basis
of Prob. Chi-
Prob. Chi-Square(3)* 0.0028 0.3153
Square(3)*
Both are heteroskedstic
Prob. Chi-Square(3) 0.000 0.0468 on basis of Prob. Chi-
Square(3)
Dependent Variable; Price
Independent Variable; Lot-size, Square-feet, Bedrooms
Constant: C
*** Sig. at 1%, ** Sig. at 5%, * Sig. at 10%, ( ) = Standard Error, [ ] = t-statistics

d.) what does this example suggest about Heteroskedasticity and transformation used for the

dependent variables.

14
 Assignment # 4

This example suggests that both models are heteroskedasticity. Informal method also shows that

there is heteroskedasticity in both models.

GENRUTSQ
5E+10

4E+10

3E+10

2E+10

1E+10

0E+00
10 20 30 40 50 60 70 80

Figure 3.1: Graph of Heteroskedasticity for Simple Model

GENRUTSQ
.6

.5

.4

.3

.2

.1

.0
10 20 30 40 50 60 70 80

Figure 3.2: Graph of Heteroskedasticity for Log(Price) Model

______________________________________________________________________________

15
 Assignment # 4

Question No 4: The file investment.xls contains data for the following variables, I=Investment,

Y=income and R=interest rate .Estimate a regression equation that has as dependent variable

investment, and as explanatory variables income and the interest rate. Check for autocorrelation

using both formal and informal methods.

Table 4.1: OLS Estimates of Investment, Income and Interest rate

Estimates
Variable Coefficient Std. Error t-Statistic Prob.
C 6.224938 2.510894 2.479172 0.0197
Y 0.769911 0.071791 10.72442 0.000
R -0.1842 0.126416 -1.45707 0.1566
Statistical Measures
R-squared 0.816282 Adjusted R-squared 0.802673
F-statistic 59.98221 Prob (F-statistic) 0.000
Dependent Variable; I=Investment
Independent Variable; Y=income and R=interest rate
Constant: C

 Table 4.1 shows that if income and interest rate are zero than still there are 6.224938
units of investment. t-calculated (2.479172) is greater than t-critical (1.645), and p-value
(0.0197) is less than 10 %, so coefficient of constant is significant at 5%.
 One unit increase in income increases 0.769911 units of investment assuming that
interest rate is constant. t-calculated (10.72442) is greater than t-critical (1.645), and p-
value (0.000) is greater than 10 %, so The coefficient of income is significant at 1%, this
leads to acceptance of H1.
 One unit increase in interest rate decreases 0.1842 units of investment assuming that
income is constant. t-calculated (1.45707) is less than t-critical (1.645), and p-value
(0.1566) is greater than 10 %, so The coefficient of interest rate is significant at 5%, this
leads to rejection of H2.
 Adjusted R-squared explains that 80.2673% variation in investment is explained by
income and interest rate.
 Probability of F-statistics (0.000) is less than 10 %, this shows that model is good fit.

16
 Assignment # 4

Autocorrelation Using both Formal and Informal Method:

Informal Method

-2

-4

-6

-8
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

I Residuals

Figure 4.1: Graph of Residuals

Graph shows that autocorrelation exist in data because most of values lies outside of certain
pattern.
Formal Method
Table 4.2: Autocorrelation
Breusch-Godfrey Serial Correlation LM Test:
Null Hypothesis: There is no serial correlation
F-statistic 6.764643 Prob. F(2,25) 0.0045
Obs*R-squared 10.53429 Prob. Chi-Square(2) 0.0052
Correlogram Q statistics
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
. |**** | . |**** | 1 0.562 0.562 10.440 0.001
. |**. | . *| . | 2 0.245 -0.103 12.490 0.002

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 Assignment # 4

Table 4.2 shows that probability of Chi-square is less than 10%, resulted in rejection of null
hypothesis. This means that there is serial correlation between residuals. Results of correlogram
Q statistics also shows that P-value is less than 10%, this lead to rejection of null hypothesis, so
autocorrelation exist in data.
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