The coefficient of each predictor variable shows us with each unit +/- in it, how our response variable changes!
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 slope of the regression equation.
b_{1} is the change in predicted value ("Number of Recruits") for each unit +/- in x_{1} ("Parties Thrown").
b_{1} = 20.5313
PRO TIP: Since there's only one coefficient & explanatory variable, that's why the problem is referring to it as the "slope" of the regression equation!
y-hat = 85.8312 + 20.5313(x)
For each additional party thrown...
y-hat = 85.8312 + 20.5313(0)
y-hat = 85.8312
y-hat = 85.8312 + 20.5313(1)
y-hat = 106.3625
y-hat = 85.8312 + 20.5313(2)
y-hat = 126.8938
...the predicted number of recruits (y-hat) is increasing by 20.5313!
Answer: With each additional party thrown last year, a fraternity's number of recruits is predicted to increase by 20.5313 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 “Posts” (b1) coefficient.
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