One of the key tasks in metropolitan area transportation planning is to estimate the total number of trips made by households during a typical day. The dependent variable is the number of trips made by a household per day, known as the trip generation rate. One of the most important determinants of variations in household trip generation rates is household income. Consider a hypothetical city, values of the trip generation rates and household income are listed in the following table. (a) Find the regression coefficients (the intercept and the slope coefficients). Interpret the meaning of the slope coefficient. (b) Write out the regression line formula. (c) Calculate the coefficient of determination for this problem.
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.
One of the key tasks in metropolitan area transportation planning is to estimate the total number of trips made by households during a typical day. The dependent variable is the number of trips made by a household per day, known as the trip generation rate. One of the most important determinants of variations in household trip generation rates is household income. Consider a hypothetical city, values of the trip generation rates and household income are listed in the following table.
(a) Find the regression coefficients (the intercept and the slope coefficients). Interpret the meaning of the slope coefficient.
(b) Write out the regression line formula.
(c) Calculate the coefficient of determination for this problem.
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