Management proposed the following regression model to predict sales at a fast-food outlet. y=β0+β1X1+β2X2+β3X3+εy=β0+β1X1+β2X2+β3X3+ε where X1X1 =number of competitors within one mile X2X2 = population within one mile (1000s) X3={1ifdrive−upwindowpresent0OtherwiseX3={1ifdrive−upwindowpresent0Otherwise YY=Sales($1000s) The following estimated regression equation was developed after 20 outlets were surveyed. y=10.1−4.9x1+6.6x2+15.9x3y=10.1−4.9x1+6.6x2+15.9x3 a. What is the expected amount of sales attributable to the drive-up window? b. Predict sales for a store with two competitors, a population of 8,000 within one mile, and no drive-up window.
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.
Management proposed the following regression model to predict sales at a fast-food outlet.
y=β0+β1X1+β2X2+β3X3+εy=β0+β1X1+β2X2+β3X3+ε
where
X1X1 =number of competitors within one mile
X2X2 = population within one mile (1000s)
X3={1ifdrive−upwindowpresent0OtherwiseX3={1ifdrive−upwindowpresent0Otherwise
YY=Sales($1000s)
The following estimated regression equation was developed after 20 outlets were surveyed.
y=10.1−4.9x1+6.6x2+15.9x3y=10.1−4.9x1+6.6x2+15.9x3
a. What is the expected amount of sales attributable to the drive-up window?
b. Predict sales for a store with two competitors, a population of 8,000 within one mile, and no drive-up window.
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