Answer to Question #100082 in Statistics and Probability for Juliet Beglaryan

Answer to Question #100082 in Statistics and Probability for Juliet Beglaryan

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Question #100082

A study was conducted to determine if larger universities tend to have more property crime. Let x represent student enrollment in thousands and let y^ represent the number of burlaries in a year on campus. ^y=1.326x-4.12. Consider university with 13000 students. a) calculate what would be the predicted number of burglries for this univeristy? b) if in fact 4 burglaries happened in this univeristy, what is residual? Is it overestimated or not? c) What is the vlaue of slope? d) if R2= 58.5% what does this mean. Calculate the correlation r and explain.

Expert’s answer

a) Given that b) The residual is The residual is negative. The model overestimates the observation (the predicted value is too big).c)If the student enrollment x increases by one thousand, then the number of burlaries for this university increases by 1.326d) R-squared (coefficient of determination) is the percentage of the dependent variable variation that a linear model explains. This means that the model explains 58.5 % of the variation of the number of burlaries. The correlation coefficient is Strong positive correlation (linear relationship).

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