Intrigued by a 2013 study at the University of Nebraska, which suggested that ma

Question

Intrigued by a 2013 study at the University of Nebraska, which suggested that marijuana smokers may be thinner than other adults, a group of students did a project to explore the relationship between body mass index (BMI) and amount of time spent under the influence of marijuana (measured in hours per week). Based on a random sample of 33 students at their university, they used BMI as the response variable. The equation of the least-squares regression line is: Hours per Month Under Influence = 49.2 - 1.15BMI Also, r^2 = 0.134. How effective is the regression model for these date? extremely effective, because 13.4% of the variation in the data is explained by the model

Explanation / Answer

r2 value tells us how much of the variation is explained by the model , it ranges from 0 to 1 and in percentage terms from 0 - 100

so here the r2 value is 0.1345

so model is able to explain only 13.45 percentage of the variation. which is infact very low . For any model to be very good the value of r2 must be above 0.9 , medium from 0.7- 0.89 and any thing less than 0.7 is considered low. However , these are not hard rules . It also depends upon the nature of the experiment and the study under which the regression analysis is performed .

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