This is an analysis that determines the relationship that exists between two variables: price and quantity demanded. (Linoff, 2008). The pizza company intends to establish a firm at the National Harbor in Washington DC. The firm carries out a regression analysis to determine the relationship between price and quantity of pizza. The sample data on the variables was collected for a period of thirty days. The simple linear regression model may be represented by the equation below:

Y= B0 + B1X

Y= Quantity of pizza.

B0= autonomous demand

B1 = Demand that depends on the price.

X= Price of a pizza.

The results of the thirty days were regressed, and the regression output is as follows.

The estimated regression model is Y= 46.17-1.91X. this means that Quantity demanded= 46.17-1.91 price.

The coefficient of determination is 0.513246 *100 = 51.3246% this means that 51.3246% of the variations in quantity are explained by the variation in the price of a pizza. The rest of the quantity variations are represented by 48.6754% , and are explained elsewhere. This means that if the pizza business establishes a firm in Washington, the quantity of pizza that people purchase will depend on the price that the firm will charge. This indicates that high prices lead to low quantity and minimal returns while low prices lead to high quantity and high profits. The coefficient of determination may be influenced by other factors that influence demand for pizza. These factors include consumer preferences, age of consumer, consumption patterns, and income of consumers (Wilson, Keating, & Beal-Hodges, 2012).

Statistical significance of price

This is found using by comparing the t-statistic with t-critical for price using the formula:

T-statistic = (B1-0)/ standard error

T-statistic = (-1.91-0)/0.35= 5.46

The hypotheses to be used for this test are

Ho:B1=0 and H1: B1 ≠0

The value for t-critical from the t-tables is 0.683 at 29 degrees of freedom and 95% level of significance. This indicates that t-statistic> t-critical hence, we reject the null hypothesis. This means that price is statistically significant.

The statistical significance of the overall regression model is calculated using the F- statistic. This is calculated by comparing the f-statistic with the f-critical. The f-critical is 4.183 while the f-statistic is 29.523. We reject the null hypothesis because f-statistic>f-critical. The overall model is significant (Wilson, Keating, & Beal-Hodges, 2012). This indicates that establishing the pizza firm is a viable decision.

The demand for the next four periods is forecasted using the prices that the firm intends to charge during these periods. In this case, the periods are days, so the next four periods refer to the next four days. The firm may decide to charge 5, 5.5, 6, and 6.5 in the next four days. The quantities that are demanded during these days may be as follows.

Y= 46.17-1.91X

Day 1= 46.17-1.91(5) = 36.62

Day 2= 46.17-1.91(5.5)=35.67

Day 3=46.17-1.91(6) =34.71

Day 4=46.17-1.91(6.5) =33.76

The company should establish the pizza operation in the area. This is because the quantity of pizza demanded has a regular variation with the price changes. The firm, however, should first carry out a feasibility study on the market for pizza. This study should cover the Washington area, to establish the prices other pizza entities charge for a pizza and other factors that affect the demand for pizzas. A feasibility study seeks to investigate market conditions and aids a firm’s management in making crucial choices affecting their businesses.

References

Linoff, G. (2008). Data analysis using SQL and Excel. Indianapolis, Ind: Wiley Pub.

Wilson, J. H., Keating, B. P., & Beal-Hodges, M. (2012). Regression analysis: Understanding and building business and economic models using Excel. New York: Business Expert Press.

Y= B0 + B1X

Y= Quantity of pizza.

B0= autonomous demand

B1 = Demand that depends on the price.

X= Price of a pizza.

The results of the thirty days were regressed, and the regression output is as follows.

The estimated regression model is Y= 46.17-1.91X. this means that Quantity demanded= 46.17-1.91 price.

The coefficient of determination is 0.513246 *100 = 51.3246% this means that 51.3246% of the variations in quantity are explained by the variation in the price of a pizza. The rest of the quantity variations are represented by 48.6754% , and are explained elsewhere. This means that if the pizza business establishes a firm in Washington, the quantity of pizza that people purchase will depend on the price that the firm will charge. This indicates that high prices lead to low quantity and minimal returns while low prices lead to high quantity and high profits. The coefficient of determination may be influenced by other factors that influence demand for pizza. These factors include consumer preferences, age of consumer, consumption patterns, and income of consumers (Wilson, Keating, & Beal-Hodges, 2012).

Statistical significance of price

This is found using by comparing the t-statistic with t-critical for price using the formula:

T-statistic = (B1-0)/ standard error

T-statistic = (-1.91-0)/0.35= 5.46

The hypotheses to be used for this test are

Ho:B1=0 and H1: B1 ≠0

The value for t-critical from the t-tables is 0.683 at 29 degrees of freedom and 95% level of significance. This indicates that t-statistic> t-critical hence, we reject the null hypothesis. This means that price is statistically significant.

The statistical significance of the overall regression model is calculated using the F- statistic. This is calculated by comparing the f-statistic with the f-critical. The f-critical is 4.183 while the f-statistic is 29.523. We reject the null hypothesis because f-statistic>f-critical. The overall model is significant (Wilson, Keating, & Beal-Hodges, 2012). This indicates that establishing the pizza firm is a viable decision.

The demand for the next four periods is forecasted using the prices that the firm intends to charge during these periods. In this case, the periods are days, so the next four periods refer to the next four days. The firm may decide to charge 5, 5.5, 6, and 6.5 in the next four days. The quantities that are demanded during these days may be as follows.

Y= 46.17-1.91X

Day 1= 46.17-1.91(5) = 36.62

Day 2= 46.17-1.91(5.5)=35.67

Day 3=46.17-1.91(6) =34.71

Day 4=46.17-1.91(6.5) =33.76

The company should establish the pizza operation in the area. This is because the quantity of pizza demanded has a regular variation with the price changes. The firm, however, should first carry out a feasibility study on the market for pizza. This study should cover the Washington area, to establish the prices other pizza entities charge for a pizza and other factors that affect the demand for pizzas. A feasibility study seeks to investigate market conditions and aids a firm’s management in making crucial choices affecting their businesses.

References

Linoff, G. (2008). Data analysis using SQL and Excel. Indianapolis, Ind: Wiley Pub.

Wilson, J. H., Keating, B. P., & Beal-Hodges, M. (2012). Regression analysis: Understanding and building business and economic models using Excel. New York: Business Expert Press.