Let's take a look at the example scatter plot representing the relationship between the $x -$ and $y -$ values.

Now, let's assume that we want to know the value of $y$ when $x = 3 .$ We cannot read this information from our plot directly. However, we can predict this value using a linear model. To do this, we need to follow three steps.

Draw a trend line.
Find an equation of the trend line.
Evaluate the equation for the particular value of $x .$

Let's start by drawing a trend line for the given scatter plot.

Next we will write an equation for our line. To do so, we need to identify the $y -$ intercept and the slope.

We can see that the

y -

intercept is

1,

so we can evaluate the slope.

\frac{Rise}{Run} = \frac{4}{5}

The slope of the line is

\frac{4}{5} .

Now we are ready to write the complete equation.

y = \frac{4}{5} x + 1

Finally, we can substitute

x = 3

into this equation and predict the corresponding

y -

value.

y = \frac{4}{5} x + 1

Substitute

$x = 3$

y = \frac{4}{5} (3) + 1

▼

Simplify right-hand side

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

y = \frac{4 \cdot 3}{5} + 1

Multiply

y = \frac{1 2}{5} + 1

CalcQuot

Calculate quotient

y = 2.4 + 1

AddTerms

Add terms

y = 3.4

We predict that the value of

y

is

3.4

when

x

equals

3 .

In general, by using a scatter plot we can make a prediction about a trend in a relationship between two quantities by following the three steps that we described.

Exercise