The following are data on the average weekly profits(in $1,000) of five restaurants, their seating capacities, andthe average daily traffic (in thousands of cars) that passestheir locations: Seating Traffic Weekly netcapacity count profitx1 x2 y120 19 23.8200 8 24.2150 12 22.0180 15 26.2240 16 33.5 (a) Assuming that the regression is linear, estimate β0, β1,and β2.(b) Use the results of part (a) to predict the averageweekly net profit of a restaurant with a seating capacityof 210 at a location where the daily traffic count averages14,000 cars.
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.
The following are data on the average weekly profits
(in $1,000) of five restaurants, their seating capacities, and
the average daily traffic (in thousands of cars) that passes
their locations:
Seating Traffic Weekly net
capacity count profit
x1 x2 y
120 19 23.8
200 8 24.2
150 12 22.0
180 15 26.2
240 16 33.5
(a) Assuming that the regression is linear, estimate β0, β1,
and β2.
(b) Use the results of part (a) to predict the average
weekly net profit of a restaurant with a seating capacity
of 210 at a location where the daily traffic count averages
14,000 cars.
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