Multiple regression model of the demand for beer in Australia
The descriptive statistics of the regression model provide that the average per capita consumption of beer is 115 liters and the per capita income is $5691.61.
The average prices of beer, wine and spirits is $1.52, $3.34 and $17.41 respectively (Table 1). The standard deviations of the per capita consumption of beer, income, price of beer, price of wine and price of spirits are 13.33, 5399.03, 1.27, 2.31 and 15.06 respectively while the total number of variables applied in the research is 42 (Table, 1).
The regression analysis for this study was done at 5 degrees of freedom. And this provides the basis for conducting the test of the level of significance for the data.
The regression models for data set are: Income Y = -4.063 X -.010, price of beer Y = -6.490 X -68.239, price of wine Y = 7.272 X + 41.922, and price of spirits Y = 2.995 X + 2.652.
The regression line for the income, Y = -4.063 X -.010, indicates that the consumption of beer is negatively related to the income of the consumers.
This also indicates that when the income of a consumer is $1 the level of consumption will be less by 4.063+.010 liters (because when x = 1 y= -4.063*1-.010). The regression line for price of beer is y = -6.490X -6.490 and this indicates that when the price of beer is $1 the consumption of beer is less by 6.490.
Additionally, consumers take less of the beer by -68.239 liters when the price is zero. The regression line for wine is price of wine Y = 7.272 X + 41.922 and this indicates that when the price of wine is $1 the level of beer is 49.194 liters while the consumers take 41.922 liters of beer when price zero.
The regression line of spirits Y = 2.995 X + 2.652 and this indicates that the consumption level of beer is 5.647 liters when price is $1. In addition, when price is zero the consumption of beer is 2.652 liters.
All the observations were significant at 5 degrees of freedom, i.e. the level of significance is less that 05 for all variables under investigation (Table, 2).
From the above regression analysis results it can be observed that when the income of consumers is low there is a decline on the level of consumption of beer as observed in the regression between consumption beer and income levels.
This indicates that consumption pattern follows that of a giffen commodity because consumers reduce the consumption of the products when their incomes are low.
Since the product is not a basic commodity consumers can reduce its consumption when their incomes are low The three range of products; beer, wine and spirits have different demand patterns.
Wine has a higher demand than any of the other products while beer has the least demand of the three products. There is a positive relationship between the consumption of beer and the price of wine and spirits whereas the consumption of beer is negatively related to the price of beer. In addition, there is a negative relationship between the consumption of beer and the income of consumers.
Conditions are required for the validity of regression analysis
- For regression analysis to be valid the independent variables are required to have independent values. This means that there should be no relationship between all the independent values.
- It should be possible to identify the independent as well as the dependent variables in the experiment.
- It is important that enough data should be collected when conducting the regression analysis.
- The relationship between variables should be easily identifiable both in visual and numbers. This means that the goodness of fit and the numbers should be easy to describe the relationship between all the variables (Wainer, Braun and Educational Testing Service, 1988).
Analysis to determine satisfaction of the conditions
All the independent variables have no relationship at all and therefore the first condition has been fulfilled. The independent variables are the per capita income, price of wine, price of beer and price of spirits. These variables have no relationship at all and this means that the regression valid on basis of the first condition.
The second conditions for validity in regression analysis require that there should be a possibility of differentiating the independent and dependent variables.
In the experiment the independent variables are per capita income, price of wine, price of beer and price of spirits. The dependent variable is the quantity of beers consumed.
In addition, sufficient data has been collected from the population to explain the relationships and this is an indication that the condition of validity has been attained. Lastly, the data is clearly visible both in figures and in the diagram.
This indicates that the regression analysis is valid. Therefore, the conditions for validity of regression analysis have been fulfilled and this shows that the regression is valid.
Reference List
Wainer, H., Braun, H., and Educational Testing Service (1988). Test Validity. New Jersey: NJ, Routledge. Appendices