A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (x), measured in Data for 21 companies who use the bank's services were used to fit the model E(y) = β0 + β1x. The results of the simple linear regression are provided below. = 2,700 + 20x Interpret the estimate of β0, the y-intercept of the line. For every $1 million increase in sales revenue, we expect a service charge to increase $2,700. All companies will be charged at least $2,700 by the bank. There is no practical interpretation since a sales revenue of $0 is a nonsensical value. About 95% of the observed service charges fall within $2,700 of the least squares line.
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.
A large national bank charges local companies for using its services. A bank official reported the results of a
E(y) = β0 + β1x.
The results of the simple linear regression are provided below.
= 2,700 + 20x
Interpret the estimate of β0, the y-intercept of the line.
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For every $1 million increase in sales revenue, we expect a service charge to increase $2,700. |
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All companies will be charged at least $2,700 by the bank. |
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There is no practical interpretation since a sales revenue of $0 is a nonsensical value. |
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About 95% of the observed service charges fall within $2,700 of the least squares line. |
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