Question

An analyst wants to determine whether the cost of a flight depends on the distance. She collects a set of data of the round-trip fare for flights between Boston and some other cities on major airlines and the distance between cities. The following table gives the descriptive statistics of the distance (in miles) and the cost (in dollars). Mean Standard Deviation Miles (x) 1650.4 1074.4 Costs (y) 291 111.71 r = 0.9352 Compute the coefficient of determination and interpret your answer.

a. 93.53% of total variations on the y-variable (Cost of the flight) can be explained by the regression line

b. 87.46% of total variations on the y-variable (Cost of the flight) can be explained by the regression line

c. There is a positive, strong linear relationship between the cost of the flight and the distance

d. There is a positive, weak linear relationship between the cost of the flight and the distance e. None of the choices

Answer 1

The idea of linear regression is to being able to predict a dependent variable from one or more independent variables. For that purpose, we are looking for a model that adjusts to the data as good as possible.

A measure of goodness of fit for a linear regression model is represented by the coefficient of determination, or R^2, and it is broadly used to assess the quality of a linear regression model.

There are various ways to find coefficient of determination, but the most simpler way is to square the correlation coefficient.

Hence R^2 = r^2

R^2 = 0.9352^2 = 0.8746

Coefficient of determination interpretation: Based on the way it is defined, the coefficient of determination is simply the ratio of the explained variation and the total variation. In other words, the coefficient of determination represents the proportion (or percentage) of variation in the dependent variable that is explained by the linear regression model.

Hence option b is correct .ie 87.46% of total variations on the y-variable (Cost of the flight) can be explained by the regression line.

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