Executive summary
This paper analysis the relationship between the cost of magazines and the number of audience, when the price of a magazine is high then the level of audience is usually high. In this analysis we hope to use econometric models based on economic theories and available literature which will enable us to specify the relationship between the dependent (audience) and the independent variable (cost per page).
In these analysis we shall also estimate and analyze the signs and magnitude of the parameters which usually have direct policy implications for a firm, organization or a government for whichever purpose they would use the data for, we have assumed that the only variable that will influence the outcome which is audience is the price per page since the percentage of males and females is just a statistical measure that is significant in this analysis since it only gives the gender differentiation as audience.
Objective
The objective of this data analysis is to establish whether there is a relationship between the cost per page and the audience, we expect to find that the higher the cost per page then the higher the level of audience, therefore our dependent variable will be audience and the independent variable will be cost per page. We expect the relationship of these variables since hypothetically we believe that if the cost per page is high and people are willing to pay for it then there must be a high audience since people expect this to a piece of quality work and thus they are ready to pay more for quality magazines that meet their expectations.
Methods
We will use the classical linear regression model to establish the regression model that will give us the relationship that exist between this two variables, we will use excel spreadsheet to do all the calculations, after getting our estimated parameters we will perform the statistical inference to determine the nature and the significance of the estimated parameters. The other important statistical inference is the correlation coefficient that will help us determine the nature of the relationship between the two variables.
Procedure
Model specification or formulation of hypothesis
We will specify our model assuming that the price per page is the only determining factor of the audience level, the audience therefore will be the dependent variable and the cost per page will be the independent variable. We expect a linear relationship whereby the two variables will have a positive relationship.
The model
Y = α + B X
Where Y is the dependent variable or the audience, α is the autonomous value, B is the slope of the model and X is the independent variable which in this case is the cost per page. We expect the slope to be positive; we also expect the autonomous value to be positive.
Estimation of the model parameters
We will estimate the regression model using the classical linear regression model, we will assume that the price per page is the only determinant of the regression model and therefore we will use simple regression analysis, the audience observation in the data is the dependent variable while the price per page is the independent variable, we exp4ect the slope of the regression model to be positive as a result of our hypothesis that the higher the cost per page then the higher is the level of audience, since we believe that the audience expect a quality magazine when the price is high and that the audience are willing to pay for the high price.
In this econometric analysis the assumption we are making is that this is a forecasting model that will be used for future planning of the EDA company, in this case we will look at the nature of the relationship as well as the relationship identification condition.
Since the purpose of this econometric research is to finds out which of the desirable characteristic is the most important eg the property of the minimum variance.
Data
The data has 51 observations and we will use all to estimate the parameters, the following diagrams are the scatter diagrams of both cost per page and audience:
The model
When we the classical linear regression model our estimated parameters give us the autonomous value as -7021.55007 and the slope of the model (B) as 0.216239403, this means that our model will take the following model:
Y = – 7021.55007 + 0.216239403 X.
Explanation of the model
To explain the autonomous estimated parameter we can say that when the price of page is zero then we expect the level of audience to be- 7021, to explain the slope coefficient we can say that when we hold all other factors constant and increase the level of prices by one unit then the level of audience will increase by 0.216239403 units. This means that the level of satisfaction the audience derive from the magazine will increase as the unit cost of magazines increase.
Evaluation of the estimates
In this stage of econometric analysis we decide whether the estimates of the parameters are theoretically meaningful or statistically satisfactory, in this stage we use three criteria modes, the first criteria is the economic criteria ( priori criteria) in this stage we look at the sign and the size of parameters of economic relationships as defined in economic theory, during this evaluation unexpected signs will lead to the rejection of the hypothesis earlier stated, this unexpected signs could be as a result of deficiencies in data especially cross sectional data and it could also be as a result of the choice of the model used.
The second is the statistical criteria or the first order test, in this stage we test the statistical reliability of the estimates, and this involves applying the correlation coefficient of the relationship between Y and X, it also involves finding the correlation of determination or the R squared.
This two tests measure the goodness of fit and the dispersion or variability, note that this criteria is secondary to economic criteria in terms of importance.
Econometric criteria or the second order test involves investigating whether the assumption of the econometric methods are satisfied or not in any particular case, it determines the reliability of the of the statistical criteria particularly the standard errors of the parameter estimates or if the estimates are BLUE (best linear unbiased estimate) this can involve a test for autocorrelation as well as a test for identification and heteroskedasticity.
For our analysis the correlation coefficient is 0.882584776, this figure is close to one, and this means there is a strong correlation between the cost per page and the audience leve, also the coefficient is positive and therefore there exist a strong positive relationship whereby and increase in the independent variable will lead to an increase in the dependent variable.
The R squared value is 0.778955887; this also shows a strong and positive relationship between the two variables, the figure is close to one and this indicates that this is almost a perfect fit meaning that the entire variation ion Y is explained by the regression line.
Valuation of the forecasting validity of the model
In this step of econometric research we test the predictive power of the model before we use it for forecasting or planning in the case of the EDA Company, we note that an economically and econometrically acceptable model may not be good for forecasting purposes because there might be rapid changes in the structural parameters of the relationship in the real world analysis.
Thus we attempt to investigate the stability or their predictive power to changes by manipulating the sample size, or the data. Incase we choose we attempt to change the data by moving from a classical linear model to a quadratic function by introducing new variables to the model eg. Our model was Y = a + bX, if we were to test the predictive power of this model qwe could device a new model by adding another variable and have a function of the form Y = a +b1X + b2Z, in this caser the Z value could be the male percentage of the audience level.
Some of the reasons that might cause poor forecasting or predicting power could be the value of the explanatory variables used in this econometric analysis may not be accurate, in addition the estimates of the coefficients of determination may be poor due to problems like specifying the model, in addition the estimates may be good for a short period of time (the period when the sample was taken) but the structural background conditions may have changed over time requiring a respecification and estimation of the model.
Analyses
In our analysis we found the relationship of the audience and cost per page to be positive and strongly correlated, this shows that the cost of magazines will determine the level of audience, the higher the price then the higher the audience. However there is need to get the sum of squares, this will involve calculating the explained sum of squares, the total sum of squares and the residue sum of square, this helps us determine the standard errors and the stochastic component.
However our results are in line with our hypothesis and through this analysis we have established the relationship between cost per page and the level of audience and our estimated model is as follows: Y = – 7021.55007 + 0.216239403 X.
Conclusions
In these analysis we estimated and analyzed the signs and magnitude of the parameters which usually have direct policy implications for a firm, organization or a government for whichever purpose they would use the data for, since we assumed that the only variable that will influence the outcome which is audience is the price per page our analysis of this model has proved our hypothesis right ( see worksheet), we assumed that the percentage of males and females was just a statistical measure that was not significant in this analysis since it only gives the gender differentiation of the audience.
The objective of this data analysis was to establish whether there is a relationship between the cost per page and the audience, the higher the cost per page then the higher the level of audience, therefore our dependent variable was audience and the independent variable will be cost per page. Work and thus they are ready to pay more for quality magazines that meet their expectations.
When we the classical linear regression model our estimated parameters give us the autonomous value as -7021.55007 and the slope of the model (B) as 0.216239403, the autonomous estimated parameter we can say that when the price of page is zero then we expect the level of audience to be- 7021, to explain the slope coefficient we can say that when we hold all other factors constant and increase the level of prices by one unit then the level of audience will increase by 0.216239403 units. This means that the level of satisfaction the audience derive from the magazine will increase as the unit cost of magazines increase.
References
Levine, Stephan, Krebiel and Berenson (2000) Statistics for Managers using Microsoft Excel, 4th edition, Mc Graw Hill, New York Description