1. Report the demographic and independent variables that are relevant to complete a demand analysis providing a rationale for the selection of the variables. The independent variables for this report will be population, average income per household, age of population, and the price of pizza. A key determinant of demand is the population of the area in question and as we will see in this report, growth will play a positive factor. The ultimate concern is can the city sustain another pizza delivery entity at its current population to restaurant ratio?
Level of income is relative to demand and typically the higher the household income the higher the demand for a product. Income levels also can influence the marginal profit for the company. Areas with higher income are willing to pay extra for a convenience of pizza delivery and typically hold more parties where pizza delivery is used as opposed to friends bringing food. Finally yet importantly is price. Given the city’s below average median house income compare to the nation, price was selected as a variable. The dependent variable is the number of pizzas sold in the area.
Using a regression model we will input the dependent variable; value of pizzas sold, along with the independent variables; population, median household income and price. We then will look then look at the summary output from the regression to make some decision about bringing a pizza store to our city. 2. Using Excel or other calculation software, input the data you collected in criterion one to calculate an estimated regression. Then, from the calculation provided, interpret the coefficient of determination, indicating how it will influence your decision to open the pizza business.
Explain any additional variables that may improve the coefficient of determination. Figure 1 City Data [pic] (Areavibes, 2012), (2010 Census Bureau, 2012), (PMQ Pizza Magazine, 2011), (The City of Homestead Florida, 2012) Figure 2 Regression Model [pic] The coefficient of determination is 93% and with adjustments, 89%. This tells me 89% of the variance of the dependent variable, pizza sold, can be explained in the changes in the independent variables; population, median household income and price of pizza. This leaves only 11% of unexplainable variables.
This shows that this regression model is dependable in making a decision as to whether to open a pizza business in this area. 3. Test the statistical significance of the variables and the regression equation, indicating how it will impact your decision to open the pizza business. We have found that the regression model is dependable, however; it is only as good as the variables that are used in the model. We must test the variables; population, income and price, to ensure as a whole there is relationship between the dependent variable, pizza sold.
This helps to determine if the prediction of the model is a pattern rather than just a chance. We will compare Significance F (. 000761528) from our model to a level of significance of . 05 (i. e. , 5 percent). This means that we have less than 5% chance of the model being wrong. Based on . 000761528 being smaller than . 05, I conclude that at the 5% level of significance a positive relationship exists between population, income, and price to pizza sold. I would continue to contemplate starting a pizza business in the city.
Forecast the demand for pizza in your community for the next four (4) months using the regression equation, including the assumptions that were used to create the demand. Justify the assumptions made related to the forecast. Using the demand function I came up with the following four (4) year forecast for pizzas sold. |Year |Sold |Population |Median Household Income |Price | |2011 |$681,300. 87 |61,240 |$29,135. 00 |$10. 00 | |2012 |$699,299. 67 |62710 |$29,362. 00 |$10. 3 | |2013 |$717,875. 11 |64215 |$29,591. 00 |$10. 06 | |2014 |$737,043. 10 |65756 |$29,822. 00 |$10. 09 | I based the population growth assumption by taking the 2011 estimation from the Census Bureau, which was 2. 4% increase from 2010, and applied to each year (Census Bureau, 2012). For the median household income, I applied . 78% increase for each year based on the average growth from 2006 to 2010. For 2011, I left the price of pizza the same and increase by . 3% thereafter.
The price of pizza over the years has not grown in comparison to population and income, however; I felt that the price should increase given basic inflation. Based on the forecasting demand, determine whether Dominos should establish a restaurant in your community. Provide a rational and support for the decision. The forecast demand was taken from a regression model that was reliable with an 89% adjusted coefficient of determination, meaning that 89% of changes in the dependent variable account for the changes in the independent variables.
The independent variables are significant based on a . 000761528 Significance F in the regression, we have, less than a 5% chance of this model given us false information. The forecast for the first year shows sales of $681,300 and $737,043 for year four. This is a steady sales increase of 2. 6%. Given the model has proved to be fit for our purpose, the data in the model has been confirmed to be adequate, the assumptions are in line with historical data, and along with the amount of forecasted sales; I believe it can be justified to establish a new Dominoes in the area.
PMQ Pizza Magazine. (2011, April). 2011 Pizza Report. Retrieved from: http://pmq. com/industryreports. php Areavibes. (2012). Retrieved from: http://www. areavibes. com/homestead-fl/cost-of-living/ Census Bureau. (2012). 2010 Census. Retrieved from: http://www. census. gov/ City of Homestead. (2012, September). Retrieved from: http://www. cityofhomestead. com/index. aspx? NID=187