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Adam’s Pizza operates in six cities in Texas and Oklahoma. The owner, Mr. Jenkins, wants to have an empirical estimation of the demand for his pizza. He plans to formulate pricing and promotion decisions for the next year, and he wants to know how price and advertising expenditure affect sales and use the results of the estimation to make a forecast for the next year (2015-1). He hired an economist to do a regression analysis. The economist collected data for 2013-1-2014-4 (quarterly) for sales, price, competitor’s price, income, and population. This data is available in Table 1 (link provided below).
The following regression model was fit to the collected data:
where Px is the price of pizza, Py is the competitor’s price, A is advertising expenditure, Y is income, Pop is population, T is trend, and is a residual or error term. Least square regression results based on the data are provided in Table 2 (link provided below).
Write a report on the findings of the regression. Include the following elements in your report:
Describe the economic meaning and statistical significance of each independent variable.
Interpret the coefficient of determination (R2).
Use a regression model and 2014 data to estimate 2015-1 sales.
Derive 95% and 99% confidence intervals for the 2015-1 estimate.
Your report must be a minimum of 2 pages in length.
Links to Data Documents
The two documents indicated above, Table 1 and Table 2, can be accessed in one Excel document via tabs at the bottom Click here to access the document. The third tab (Table 3) also provides information for this assignment. Table 1 is organized to run a regression.
Business Analysis
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Business Analysis
In this scenario, there are six different, and independent variables and regressions, namely the Pizza’s price, competitor’s price, expenditure acquired from advertising, income acquired, population, and finally, the trend established. Primarily, the coefficient of pizza’s worth is -1222607 and value p_ value is 0.00000000365. These values indicate that if, in any case, a unit increases the price of the pizza, then it is likely that the demand price will decrease 122607 times. The value p_ value, which is 0.00000000365, is less than 0.05 shows that the demand for pizza is affected profoundly and significantly by the independent variable price of the pizza. This is because, if the p_ value is less than 0.05, the regression is considered significant; however, if it is higher than the alpha=0.05, the regression is insignificant. Secondly, the competitor’s price coefficient is 5.8 and a p_ value of 0.00102. This means that if the competitor increases the price with a single unit, then the demand price increases 5.84 times. On the other hand, the p_ value is 0.00102, which is less than 0.05, means that the independent variable price of the competitor affects the pizza’s demand significantly.
Expenditure used in advertising records 29867 and a p_ value of 0.03196. This translates to; if the advertising expenditure is increased with a unit, the demand price increases 29687 times. On the other hand, the p_ value of 0.03196 shows that the competitor’s price has paramount effect on the pizza’s demand, as it is less than 0.05. On income variable, a coefficient of 2.04 shows that every time a unit increases on the stated income, the demand price increases 2.04 times. More importantly, a p_ value of 0.5901 is higher than 0.05, hence, concluding that the independent variable (income) lacks any critical effect on the demand of the pizzas. The coefficient of the population variable is 0.03026 and 0.00000000189 p_ value, which indicates that if population increased by a unit, the demand price would increase 0.03026 times. Hence, population has a significant effect on the demand price of pizzas since the p_ value is less than 0.05. Finally, the trend’s coefficient is 3097, and the p_ value being 0.5385. The independent value has a higher p_ value hence has lesser or no significant effect on the demand price of pizza. An increased unit of the variable would result in an increased demand price 3097 times.
The coefficient of determination is used to determine and assess if the model used to explain and predict future outcomes are good or ill fit. The measure ranges between 0 and 1, whereby when the value is closer to 1, the variable is predictable and without error, indicating that the model fitting is proper as it provides a significant effect. However, if the value is closer to 0, the regression is insignificant, and the model fitting is not suitable. The coefficient of determination R square (R2) is 0.87104, which is closer to one 1 making the regression significant for the data presented. Therefore, 87% of this variation is explainable through the model.
The 95% and 99% confidence interval for this scenario and sample is between 581747.7 and 58754.3, which is acquired as seen below.
Using the regression equation and using the 2014-4 data, the value would be = 582751-1222607*8.745+5.84*33535.7+29867*6.259+2.04*58558.5+0.03026*5989920.2+3097*8. The demand price of pizzas in year 2015-1 would be -9400671. Using this information, 95% and 97% confidence intervals would be estimated using sample statistics, selecting the confidence label, and finally finding the critical value. From the output derived in the regression, the slope coefficient is 582751, and the confidence level is provided, which is 95%. The critical value will help compute and derive an error margin as well as a degree of freedom. Hence,
a= 1- (cl/100) = 1-(95%/100%)
= 0.05.
The critical probability (p*) = 1-0.05/2 = 0.975.
DF = n-2
= 48-46
= 2
Using 46 as the DF, a p* of 0.975, and the t distribution calculator, the critical value (t) is 2.01. Therefore, error margin (ME) = critical value (2.01) * standard error (499.16) = 1003.3. The range was achieved by adding the CF sample and the margin error.
