Shan Foods estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April: Q = - 10,400 - 84P + 40PX + 10.4 l + 0.40 A + 0.50 M (4.002) (34.5) (12.2) (5.04) (0.18) (0.42)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Shan Foods estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:
Q = - 10,400 - 84P + 40PX + 10.4 l + 0.40 A + 0.50 M
(4.002) (34.5) (12.2) (5.04) (0.18) (0.42)
R2 = 0.67 n = 47 F = 3.78
Assume the following values for the independent variables:
Q = Quantity sold per month
P(in cents) = Price of the product = 1000
PX (in cents) =Price of leading competitor’s product = 1200
I(in dollars) = Per capita income of residents = 11,000
A (in dollars) = Monthly advertising expenditure = 20,000
M = Number of microwave ovens sold in the SMSA in which the supermarket is located = 10,000
Using this information, answer the following questions:
- Compute T stats of each variable
- Compute elasticities for each variable.
- How concerned do you think this company would be about the impact of a recession on its sales? Explain.
- Do you think that this firm should cut its price to increase its market share? Explain.
e. What proportion of the variation in sales is explained by the independent variables in the equations? How confident are you about this answer?
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