# An eccentric professor believes that a child with IQ 95 should have reading score 70. What is the equation of the professor's regression line for predicting reading score from IQ?

## She also believes that the reading score should increase by 2 point for every additional point of IQ.

Jun 7, 2017

$y = 2 x - 120$

#### Explanation:

A linear regression line has an equation in the form $y = b x - a$, where
$a =$ the y-intercept (if x=0, what does y=?)
$b =$ the gradient
$x =$ the independent variable
$y =$ the dependent variable

In this question, the first thing to do is identify $y$ and $x$. From the question, we see this: "reading score should increase by 2 point for every additional point of IQ." What this is telling us is that the reading score is the dependent value, since it only increases or decreases based on what the IQ is. Vice versa, that means the IQ score is the independent value. So from that we have our first 2 values,
$x =$ the IQ
$y =$ the reading score

The next thing to do is to find $b$, the gradient. We read the question, and this sentence jumps out at us again; "reading score should increase by 2 point for every additional point of IQ." What this is saying is that for every IQ point, there are two reading score points. Substitute in $y$ and $x$, and we get $y = 2 x$. This makes 2 the gradient, so $b = 2$.

Let u now put our equation together, so it looks like
$y = 2 x + a$. The only thing left to do is find $a$. To do that, we substitute $x$ and $y$ for two of their value, 95 and 70, so that we get
$70 = 2 \cdot 95 + a$
$70 = 190 + a$. The only thing left to do, is find $a$. First we subtract 190 from both sides, so we are left with
$- 120 = a$ . And there is the answer, $a = - 120$. Put that into the regression line, and the final equation is
$y = 2 x - 120$

I hope I helped!