The y-intercept shows us what the response variable would equal if the explanatory variable(s) were zero.
Scenario: Crammer Nation University wants to develop a regression equation to predict the number of recruits a given fraternity will receive this rush season given the number of parties that fraternity threw last year. The took a sample of 52 fraternities on campus, resulting in the regression output below.
Interpret the y-intercept.
b_{0} is the y-intercept.
b_{0} = 85.8312
y-hat = 85.8312 + 20.5313(x_{1})
x_{1} = 0
y-hat = 85.8312 + 20.5313(0)
y-hat = 85.8312 + 0
y-hat = 85.8312
Answer: If a fraternity threw 0 parties the previous year, they are predicted to receive 85.8312 recruits this rush season.
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Your university wants to predict the “Sign-Ups” at a student organization receives at mega fair based on the social media “Posts” made by that organization throughout the semester. They sample 30 student organizations, resulting in the following regression analysis.
Interpret the meaning of the “Intercept” (b0) coefficient.
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