The UK’s ever increasing population has put vast pressure on the housing market. “On the 1st of January this year 64.8million people were living in the UK,” (Dawar, 2015) which has been thought to have put the UK into a population overload. Figures based on stats from the Office for National Statistics show a UK population growth of more than 400,000 just in the last year. This is merely one factor that affects UK house prices, Economic growth or real income determines ones' eligibility to spend on buying a house, according to (Pettinger, 2011), the correlation between the house prices and the wealth of its owners is directly proportional. This is due to the fact that more wealth will mean a higher disposable income which in turn will increase a consumer’s confidence and spending in economic activities. However, the ratio between house prices and income can vary vastly. An example being between 1995 and 2007 the ratio between house prices showed a significant increase (Pettinger, 2011). However, a significant decrease was also seen in the UK during the Great Recession between the 2nd quarter of 2008 and 2nd quarter of 2009 where unemployment rates soared and the demand for buying houses fell drastically. This also meant house prices dropped making them more affordable but buyers were faced with the problem of tighter lending criteria by lenders, such as higher deposits as they tried to be cautious.
Increasing population leads us on to supplying demand, there are many reasons behind limited supply, the most straightforward would be when house prices rise, there will be a correlative lack in demand for supply. Councils can also choose to restrict the number of new houses built, this could be to increase prices of existing homes in the area. On the other hand, the government have implemented plans to deal with the issue of increasing the supply of housing. In 2007 the parliament set a target of 240,000 new builds by 2016, this was then put under severe pressure due to the impact of the credit crunch which hit the UK not long after.
The unpredictability of interest rates also makes predicting mortgage payments somewhat difficult, with interest rates and monthly repayment being the focal point of most mortgages, most homeowners will choose a variable mortgage where monthly repayments will fluctuate with the Bank of England base rate changes. This would mostly put off a lot of buyers, as ever when a fixed rate mortgage is offered the protection from fluctuating rates will be between 5-10years.
This paper will analyse the volatility of house prices in relation to the following variables: Gross Domestic Product of the UK economy, disposable income, unemployment, interest rates, mortgage availability, construction cost, and population.
1. Contextual Background
In August 2007 the world woke up to news of a severe shortage of money/credit, this global financial issue also known as the ‘credit crunch,’ was the start of a massive financial and economic crisis for the UK. This crisis saw people lose their jobs, people that got to keep their jobs had to accept a pay freeze and most of all Interest rates were drastically cut affecting a lot of savers. On the other hand, house prices were seen to drop drastically with Nationwide (Building Society) reporting a 6.3% drop in house prices in July 2008. This drop in house prices was consistent throughout the entire credit crunch.
Moreover, the credit crunch turned into a deep recession, in fact a double dip recession, which saw the collapse of business’, a drop of around 4% of the economy in comparison to the third quarter of 2007. And just when everyone thought how long could it go on for? ‘After five years, we are in a worse place than when we started,’ wrote Jamil Baz, who was the chief investment strategist at hedge fund GLG, during an analysis in July 2012. His observations showed that the total debt, which covered the government, household, financial and corporate debt was actually higher than it was in 2007. This credit crunch now turned double dip recession saw a fall in the GDP, a fall in GDP will cause a rise in unemployment, as business will go bankrupt or in a bid to reduce costs business will make cuts on hiring new employees and also lower wages.
The graph above shows the impact on employment levels within the UK between 2008-2014, with particular emphasis on the period 2008-2012 which defines the worst hit times. The 2nd quarter of 2012 shows the start of a steady rise in employment. During the period of 2008-2014 the government saw a fall in tax revenue as a result. This was due to:
• Businesses making less profit, which means lower corporation tax
• Employees would have also had their pays cut, resulting in a low income; in turn they would be paying less tax.
• Lower spending of the UK economy resulting is lower VAT payments.
The entire negative cut backs on taxation would be further affected by the rise in government spending on welfare/benefits. As more and more people will be claiming unemployment benefits, income support and social housing.
All the above problems coupled with tighter lending criteria’s saw mortgage lending fall making it difficult for first-time buyers to step onto the property ladder. Proving rather beneficial for wealthy customers looking to make the most of the drop in house prices, which saw a surge in buy-to-let mortgages which weren’t affected so much by the tighter lending criteria.
The rest of the paper will analyse findings from previous literature, along with methodology, data and results to demonstrate the effects various determinants have had on UK house prices.
2. Literature Review
There have been substantial studies and research papers in relation to the determinants of house prices. Previous Literature will be reviewed in order to understand other author’s perspectives on this issue as well study their different channels of research. Commenting on the conclusions they reached based on their results and how this could directly or indirectly apply towards this paper. This will aid me in understanding the different determinants of house prices and depending on the times the studies were carried out; it will also help me develop further knowledge of issues that could have occurred between certain periods of time.
2.1. The Effects of Economic Growth on UK house prices
When looking at economic growth of house prices, two important factors are usually given consideration: Inflation & Gross Domestic Product. Gross Domestic Product (GDP) is a measure of national income / national output and national expenditure produce in a particular country. According to Pettinger (2011), the correlation between the house prices and the wealth of its owners is directly proportional. This is because it will create more confidence to their spending habits, which leads to an increase in credit card borrowings. Banks also tend to be more linear when householders request higher loan amounts. ‘If house prices rise, then the wealth effect is likely to cause an increase in consumer spending’ (Pettinger, 2011) which causes higher aggregate demand and eventually an increase in Real GDP and therefore a higher rate of economic growth. This multiplier effect illustrates how house prices have an effect on an individual that leads to a change in the whole economies growth rate, which differs, from its initial effect. This may add pressure to inflation causing it to rise, due to the rise in consumer index.
Inflation is defined as the increase in the price of goods and services in a particular economy over a period of time (Investopedia, WII). According to Tsatsarinis and Zhu (2004), Inflation has a crucial influence on house prices, Egert and Mihaljek (2007), have also found a robust relationship between real interest rates and house prices. With inflation accounting for more than half of the total variation in house prices. One particular explanation for inflation being an influential factor could be the impact of inflation on the cost of mortgage financing, suggesting higher inflation will increase house prices. A recent example of this was seen during the recession when inflation rates dropped causing a drop in house prices, however due to building societies creating tighter lending criteria’s it still made it difficult for first time buyers to step on the property ladder.
2.2. The Effects of Interest Rates on UK house prices
This bring us onto Real Interest Rates, which can be defined as a formula:
Real Interest Rate = Inflation + Interest Rate
Real Interest rates share strong links with income; Benamraoui (2010) and Berglund (2007), state that their findings have shown, real interest rates and earnings, have the highest correlation with house prices. Findings of Egert and Mihaljek (2007) show that the obtained nominal interest rate elasticity’s were either positive or statistically insignificant.
Moreover, studying this determinant further shows that with a fixed mortgage rate a decrease in real interest rates lead over time to increases in house prices, (Tsatsarinis and Zhu, 2004). This point is closely supported by Harris (1989) who explains that, ‘the real rate of interest from a buyer’s point of view would be the primary mechanism, affecting change in prices as the nominal interest rate is slow to reflect changes, whereas real interest rates vary over time’. This is further supported by the findings of Egert and Mihaljek (2007) who explain, as income grew, real interest continued to fall which in turn caused nominal house prices in Central European countries to grow at double digit annual rates. However, with floating mortgage rates the impact of short-term adjustment on interest rates is much stronger on house prices. Floating mortgage rates are commonly used in countries such as Australia, Ireland, Norway and Sweden (Tsatsarinis and Zhu, 2004).
On the other hand, referring back to Harris (1989) he also provides a counter argument favouring nominal interest when evaluating investment returns; ‘when nominal interest rates rose, decreased affordability hit the market causing a disadvantage to buyers. Furthermore, when prices responded, expectations turned downward’. Drake (2003) argues that real interest rates are influential but not as much as some other determinants, in particular disposable income. However, the sample length of Drake’s research, which is between 1981-1990, could be questioned as somewhat modest. Furthermore, looking back at the economic state of the UK, the early UK recession of the 1980s and 1990s the recession was over by Q1 and Q3 consecutive.
Reading further Schwab (1981), Tsatsarinis and Zhu (2004) and Sutton (2002) state that their findings show favourable results when using nominal interest in comparison to real interest rates in regressions. Which makes sense when considering this fact from a building societies point of view, where the decision to grant a mortgage would depend on the income and the size of loan, which would be purely dependent on nominal interest rates. Finally, Meen (1999), explains in the case of an efficient market, real interest should be used as an explanatory variable but, due to the lack of efficiency and information about the rate of inflation, data is not easily obtained. This can now be challenged, as currently data is readily available via a variety of sources in 2016.
2.3. The Effects of Disposable Income on UK house prices
Disposable income has key significance when it comes to house prices, it holds the key to mortgage eligibility. In fact, demand for housing is noted to be income elastic, where rises in income are known to cause a rise in money being spent on houses (Bergland, 2008). Disposable income was used, rather than personal income, as the amount spent on housing is normally calculated by the householder and often by the building society as a proportion of money available to spend after taxes, rather than out of total income (Whitehead, 1974).
Disposable income is the most influential factor (Drake 1993). This statement has been proven by many authors and researchers. Benamraoui (2010); Egert and Mihaljek (2007); Giussani and Hadjimatheou (1992) have found positive correlation between the rise of house prices in line with disposable income. With Holly and Jones (1997) recording correlation over the last 60years, Making disposable income ‘the single most important determinant.’ Another paper which was particularly interesting was Meen (2002) who tested for cointegration using national-level data, with the results showing no significant evidence of cointegration. However, Meen states that his findings are close to the critical values, concluding house prices and fundamentals are cointegrated. The inverse of the pro disposable income argument was seen during the recent recession when disposable income dropped as a result of pay cuts and unemployment which saw a drop in house prices.
By contrast some authors argue against disposable income being such an influential factor on house prices. Tsatsarinis and Zhu, (2004) have found a very small effect on house price movement with close agreement from Egert and Mihaljek (2003) that in recent years the reason for the booming housing market in the UK are factors other than disposable income. Gallin (2003, P.2) in particular found some interesting results; from mid 1997 to mid 2002, real house prices have risen about 28% whilst income rose around 15%. Which implies the lack of cointegration between income and house prices, therefore rendering this determinant useless in predicting future movement in house prices. However, Gallin’s research can be argued against as cointegration tests which involve small samples are known to have low power (Banerjee, 1999).
2.4. The supply and demand of dwellings and its effects on UK house prices
The supply of new dwellings is something the UK has been slacking on since late 1970s. Although it has only been highlighted recently after widespread political attention, it’s been obvious that successive governments have failed to meet the demand of housing. This increase in demand is due to a few factors such as growing migration, prolonged life expectancy and the increase in one-person households. Other factors such as higher income have also been seen to increase demand for new housing, (Glindro, Subhanij, Szeto, and Zhu, 2008). Failure to meet rising demands has resulted in rising average prices and also volatility of house prices as seen during the last 30years. Two crashes in house prices between 1990-1992 and the most recent being 2007-2010.
With the UK population projected to increase by 9.7million over the next 25years (Pettinger, 2015), Population is probably one of the major reasons for the rise in demand of dwellings. The reason for this population increase is migration and higher birth rates, but by mid-2039 more than 1 in 12 of the population have been projected to be over the age of 80 (Pettinger ,2015). This can increase current demands on government spending such as health and pensions leading to lower tax revenues. However economic rewards can also be reaped, as migrants will add to the total spending within the economy. This increase in spending will result in an increase in supply of labour, to meet the increase in demand for labour. This could also be opposed by Britain’s generous welfare system, with many migrants that end up receiving benefits and requiring housing.
Certain economic factors have also put pressure on these targets being met; the onset of the credit crunch in 2007 was certainly a big draw back. Although demands rose during this period, the difficulties faced with gaining credit, saw builders reduce the supply of new houses. Wheaton and DiPasquale, (1996) have mentioned that the supply of new housing can be affected by changes in government regulations or changes in short –term interest rates, with the later point being appropriate in this case.
House prices can also rise over time due to construction costs (Reichert, 1990). Builders will always pass on a percentage of the rising construction costs, which can all be a direct result of effects in wages, material costs and financing costs. They will also have to factor in a percentage for any risk that can be faced as the spread between expected selling price and buildings costs widen. A key observation that has been made whilst studying a variety of research papers is the fact that a higher interest rate depresses both the supply and demand of dwellings, (Barot and Yang 2002). This is partly supported by recent events during the recession which saw interest rates plunge however a positive demand was still seen. However, when interest rates drop in a perfect economic situation, ‘a positive increase in the supply of houses will be noticed. Increased supply will lead to lower cost of ownership and lower prices on the housing market’ (Berglund 2007).
3. Data
Recalling the key determinates, the independent variables are: Real GDP growth, Real Disposable Income, Building Society Average Mortgage Interest Rates, Population growth and Completed Dwellings; the dependent variable being the Real House Price. Quarterly data from the first quarter of 1980 to the last quarter of 2014 for the UK has been obtained to justify this time-series analysis. The paper has used a variety of sources to extract the statistics, these include OECD, The World Bank, www.gov.uk, www.dallasfed.org and DataStream. Data collected from these databases are official and trustworthy and therefore assures that data was not altered that may produce inaccurate results.
Quarterly data was easily available for all variable’s apart from population which was only present annually. The total observation is 140 observations initially, but some results have been lost as a result of transformation. The date range has been chosen to ensure it comprises both historical and recent trends to cover a broader aspect. The frequency, to achieve precise results as possible. The reason why monthly data has not been used is because the frequency available on some variables were too large i.e. annually and hence the transformation will be large and results could be affected and be inaccurate. In the following sub-sections this paper will discuss the variables used and what it hopes to achieve. This research uses real terms based on previous literature as it takes into account of inflation, as evidence proof the use of nominal data gives insignificant results (Ashworth and Parker, 1997; Benamraoui, 2010; Berglund, 2007 and Egert and Mihaljek, 2007).
The natural logarithm is taken for RHPI, RPDI, MIR, and SUP to reduce heteroscedasticity where possible. Logs reduces the variance and the range in some cases of the data. It also ‘makes estimates less sensitive to outlying observations’ (Wooldridge, 2008, p.191) on the variables. This is also one of the assumption for the OLS model.
3.1. Key Variables & Descriptive Statistics
The dependent variable, Log Real House Price (RHPI) is measured in the form of index, the base year is 2005 with the base value of 100, the use of index allows data to be compared more easily. Graph 1. in Appendix A, illustrates a positive upward trend in house prices with three phases where there was a major drop. In the 1980’s a result of financial liberalisation (Muellbauer and Murphy, 1997), then the housing crises in the early 1990’s and the most recent, during the financial crises between 2008-2010. The data was collected from www.dallasfed.org.
The first independent variable, Real Gross Domestic Product growth (GDPG) which shows the percentage change of the ‘national’s overall economic activity’ (Investopedia.com, 2003). As this is the growth rate from one period to another graph 2, for GDPG (see Appendix A) appears to be stationary, however, before making these assumptions, some test must be conducted to verify this. Also, GDPG tends to drop drastically during the above mentioned periods indicating a possible relationship between the house prices and GDP itself. Statistics were collected from the official OECD website.
Real Disposable Personal Income (RPDI) is the next variable, this takes into account the affordability of a buyer. Again this is measured in index and figures were taken from www.dallasfed.org. RPDI should move along with house prices in a cointegrated manner according to previous findings. As plotted on the graph (3) in Appendix A for LOG_RPDI, the points move in a positive trend. On the other hand, the data does not seem to fluctuate massively in comparison to house prices which earlier research evidently described RPDI being a significant determinant.
The Average Building Society Mortgage Rate (MIR), is one that moves in the opposite direction in contrast with house price but remains consistent to historical trends. Rates were obtained using DataStream and these are in percentages. As seen in the graph 4 (see Appendix A), after 1990’s MIR continuously decreased as house price rose. Similarly, during the bust in the housing markets, MIR also dropped. Thus we expect to achieve a negative correlation with RHPI.
The Supply of Dwellings (SUP) is measured in units and indicates the total number of completed houses over each quarter. In Appendix A, one can see that these have significantly dropped and perhaps why RHPI have increased in value. The numbers were obtained from the official www.gov.org website. A notable drop occurred during the 2008-2010 recession, however, the trend does seem to increase during the recent years but this remains unclear and difficult to measure until dwellings are actually completed.
The last variable is the Population growth (POPG), regardless of any recessions and/or recent increase as a result of migrant crises, this variable has been increasing contemporaneously. The graph (see Appendix A) shows a positive correlation with house prices accepting Reichert (1990) findings that an increase in growth would add pressure to the demand for housing. The numbers have been obtained from the world bank database, however, only yearly data was available. Thus, the statistics have been transformed into a quarterly frequency using the liner-match interpolation method. This could potentially lead to inaccuracy and dubious results later on. On the positive aspect, the proxy allows this study to be consistent with the rest of the variables and results can be interpreted in a more understandable aspect.
3.2. Correlation Analysis
It is important to pay attention to the relationships between one independent variable to another prior to the use of OLS. If two explanatory variables are in exact linear function of one another (correlation between them is either close to or is -1 or +1) it is referred to the existence of multicollinearity. If this exist, the OLS method used would fail leading to insignificant results. To limit the effect of multicollinearity, variables that have a high correlation can be dropped out the model, however this will be biased. Nevertheless, precautions can be made when making comments specifically on the ones with high correlation.
Table 1, represents the correlation matrix and this displays some signs of collinearity between all independent variable. However, most are lower than 0.70 and greater than -0.70. Arguably, there is some strong positive correlation of 0.8795 between the natural logarithm of POPG and natural logarithm of RPDI and fairly negative correlation of -0.8458 between natural logarithm of POPG and natural logarithm of MIR. Also a negative correlation between natural logarithm of MIR and natural logarithm of RPDI (-0.8990) is present. Supporting with evidence, this paper will continue to use all the regressor’s presented initially in this study taking extra attention towards the LOG_MIR & LOG_RPDI, LOG_RPDI & POPG and POPG & LOG_SUP.
Table 1: Correlation matrix
Correlation
GDPG
LOG_RPDI
LOG_MIR
LOG_SUP
POPG
GDPG
1
LOG_RPDI
-0.0560
1
LOG_MIR
-0.0155
-0.8990
1
LOG_SUP
0.0404
-0.5107
0.6587
1
POPG
-0.1780
0.8795
-0.8458
-0.4690
1
4. Methodology & Results
The next section will thoroughly explain each step and method used to obtain a successful model which then can be used to forecast future house prices. The Augmented Dickey-Fuller (ADF) test, Ordinary Least Square (OLS) model and Autoregressive Distributed Lag (ARDL) Model are the main techniques discussed and their results will be interpreted within each sub-section. A brief robustness check is conducted on the final model to check for serial correlation, homoscedasticity and whether residuals are normally distributed around the mean.
4.1. Unit Root Test & Stationarity
Before conducting an OLS regression, it is important to understand whether a time-series is stationary or non-stationary to avoid regressions being spurious. That is, when two or more independent variables show ‘apparent significant regression results from unrelated data when non-stationary series are used’ (Carter et al, 2012, p.482). Therefore, non-stationary time-series are unpredictable and can result to model misspecification later on. To avoid this, a unit root test must be performed.
Majority of the data used within this study show a non-stationary behaviour, therefore, it is necessary to conduct a unit root test for stationarity. In this research, a popular method known as the Augmented Dickey Fuller (ADF) Test will be used. The null hypothesis is rejected indicating a stationary series when test statistic is less than the critical value ( ≤ c). On the other hand, if the critical value is greater than the test statistic ( > c), we accept the null hypothesis, that the series is non-stationary. Furthermore, if results denote non-stationarity, the variables needs to be transformed into a stationary series by making the series first differenced (, this is also referred as integration of order one I(1).
4.2. Unit Root Test – Results
Table 2 represent all variables both at I(0) and I(1), results are rounded to four decimal places for reliable interpretation as the number's are relatively small. Results suggest that RHPI, RPDI, MIR and SUP were non-stationary implying the null hypothesis was not rejected. The p-value for these were greater at 5% critical level and hence must be made stationary by taking the first difference. Surprisingly results for POPG prove significance at 10% critical value (p-value < 0.10), although, the graph for POPG (see Appendix A) visually indicates non-stationarity. Thus indicating the importance of unit root tests. GDPG at I(0) is stationary with p-value being less than 0.05 and therefore it is not required to be differenced. Once the non-stationary variables have been first differenced, results prove (see table 2) that all variables are stationary with p-values holding values less than 0.05.
TABLE 2: UNIT ROOT TEST results
Variables
Without Differenced i(0)
First Differenced I(1) (∆Variables)
Test Statistic
Test Statistic
ADF
P-Value
ADF
P-Value
Log Real House Price Index
-3.1343
0.1027
-3.5290
0.0005***
Real GDP growth (%)
-6.4968
0.0000***
–
–
Log Real Personal Disposable Income
0.7385
0.9997
-9.4322
0.0000***
Log Mortgage Interest Rates (%)
-3.1265
0.1044
-8.8652
0.0000***
Log Completed Dwellings (units)
-3.0003
0.1360
-4.7800
0.0000***
Population growth (%)
-3.2043
0.0879*
-2.7962
0.0054***
Note: *, ** and *** indicate 10%, 5% and 1% critical levels.
4.3. The Ordinary Least Square (OLS) Model
We begin by using a simple OLS model to estimate this time-series process. Firstly, certain properties of OLS under the classical assumptions must be covered and met that will aid us to create a successful model which then can be used to forecast.
The assumption for no perfect collinearity and homoscedasticity was discussed in earlier section. Other assumptions include that the stochastic process follows a model that is: ‘linear in parameters’ and ‘the expected value of the error term, given the explanatory variables for all time periods is zero’ (Wooldridge, 2008, p.347). The model should also have no serial correlation and residuals should be normally distributed around their mean. One important factor the OLS demonstrates is that the estimates provide parameters that minimises the sum of the squared residuals which finds the differences between the predicted dependent variable (natural logarithm of RHPI) and the actual dependent variable.
In order to formulate an appropriate OLS model, lets remind us that the the function of house prices in this study is as follows:
Model 1:
where RHPI indicates Real House Price to be a function of Gross Domestic Product growth (GDPD), Real Disposable Income (RPDI), Mortgage Interest Rates (MIR), Completed Dwellings (SUP) and Population growth (POPG).
Therefore, the corresponding econometric model is as follows:
Model 2:
Where denotes variables being first differenced where applicable and the natural logarithm is expressed as for particular variable. is the error term and the subscript ‘t’ represents a particular point at time, t. is a constant term and where symbolises the coefficients for ‘k’ number of parameters. These constraints remain constant throughout this paper unless stated otherwise.
In order to be in line with previous studies, this paper expects to have a positive effect on house prices for the following control variables: GDPG, RPDI and POPG and a negative correlation for MIR, and SUP if the model has been regressed successfully considering we take precaution of MIR, POPG and RPDI as these tend to have a high correlation with other explanatory variables. Also RPDI should obtain the highest coefficient out of all variables. To confirm these predictions, we will look at the following characteristics to comment on the success of a model.
4.3.1. T-statistics
To check for significance, the test statistic value is observed and if the p-value is greater than 0.05, it is said to be insignificant therefore we reject the null hypothesis, whereas it is significant if the p-value is less than 0.05 meaning that the independent variable has an effect on house prices.
4.3.2. The Goodness of Fit (R2) and Adjusted R2
R2 is a measure of the goodness of fit by measuring ‘how close the data are to the fitted regression line.’ (Frost, 2013) however, this paper will observe the value for the Adjusted R2 as it adjusts ‘for the number of predictors in the model’ (Frost, 2013) and only increases if the new variable increases the reliability of the model more than just by chance. Therefore, the higher the adjusted R2 the better the model is.
4.3.3. F-Statistics
Measures the joint probability of the explanatory variables and indicates whether these together have an influence on the dependent variable and the following formula is used to:
where the critical values are given by F(K-1,N-K).
4.3.4. The Durbin-Watson statistic
The Durbin-Watson statistics is a number that checks for autocorrelation inn the residuals. The statistic is always between 0 and 4 and 2 indicating no autocorrelation whereas a number close to 0 represent positive autocorrelation and number approaching 4 denoting negative autocorrelation.
4.4. Initial Results
Table 3 shows the initial results of the regression; these seem somewhat both consistent and inconsistent with previous theory. The variables ∆LOG_MIR, ∆LOG_SUP and ∆POPG are insignificant and disregard with past research. On the other hand, both GDPG and ∆LOG_RPDI show significance at 1%. Favorably, ∆LOG_RPDI has the highest coefficient of 0.7203 and is also positive correlated to house price. This agrees with previous findings (Drake, 1993; Benamraoui, 2010; Egert and Mihaljek 2007; Giussani and Hadjimatheou, 1992) and thus confirms that RPDI is one of the influential determinants of house prices. The adjusted R-squared is relatively very low indicating a weak model and claiming that RHPI is explained by residuals and other variables other than from those explanatory variable originally included. The Durbin-Watson is 1.3680 indicating some positive serial correlation. The F-statistics would be overlooked at this stage as t-statistics for three explanatory variables remain insignificant.