Linear Regression Analysis I am very new to linear regression analysis and I am trying to solve my first examples, most of the examples I have come across contained some tables and data where I could easily use the formulas I know and solve them. However, I have just come across an example that does not have much data and I have no idea where I should start and which formulas I should use to initiate.
we assume that the number of schoolchildren's close relationship has a linear association with the likelihood (0-100%) that a child becomes bullied in the classroom. We build a regression model where we predict the likelihood of becoming bullied with the number of friends. We found out that if a child has no friends, the likelihood of being bullied is 70%. We also know that the regression coefficient (beta) for the variable 'number of friends' is -10.
This question is asking me to write the regression equation and also predict the likelihood of being bullied if the child has 14 friends.
Shouldn't I simply use the following formula? But isn't something missing in the question?
ŷ = β0 + β1x
 A: Simple illustration to know why the linear regression in this case does not work , and what is the logistic regression .
First of all , you have to know that your dependent variable $y$ (child becomes bullied ) is a binary variable , that means it takes two outcomes either Yes (becomes bullied ) or No (does not become bullied ).Let us create a dummy variable to indicate if an observation yes or no :
$y=1$ if yes 
$y=0$ if no
In the example we want to know what determines that a child becomes bullied , our independent variable  in this case is the number of friends $x$
Suppose that we run the regression model:
$Yes(y=1) =\alpha +\beta{x_i} + error$ 
Now suppose we got the following outputs
$yes=-1+0.5{x_i}$
Since our dependent variable is binary , that means we  want to know what makes it  change from 0 to 1 , in other words , we want to know what increase the likelihood of being bullied $Pr(y=1)$
So our model could be 
$Pr(y=1)=-1+0.5{x_i}$
Now can you calculate the likelihood that a child being bullied who  has 25 friends ?.I suppose ,you know that the probability is bounded wherby   $0\leq p \leq 1$.
If you get a strange result you have to find out a function which satisfies  this condition $0\leq p \leq 1$ (squared function or exponential function..etc)
A: If it doesn't have much data you may have a problem.
If your data on bullying consists of a yes/no variable (bullied vs. not) for each child, then @JimBoy is right and you should use logistic regression. If you haven't studied that yet, then you should either do so or look for a different problem.  Linear regression (which is what people usually mean when they just say "regression") is for dependent variables that are continuous - that is, they can take on any value. 
If you tell us what data the example you are using does supply, we may be able to give a more comprehensive answer
A: Using the linear probability model (*), you can solve your problem using the given equation. When you've used the values to make a prediction, you'll probably get an unexpected likelihood (hint: what are the range of possible likelihoods? can they be negative?), which is one of the reasons why you'll learn logistic regression. Sometimes though this model can be usefull as well.
(*) https://en.wikipedia.org/wiki/Linear_probability_model
