Exercise 1 Page 226

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.

1. Draw a trend line.
2. Find an equation of the trend line.
3. 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. Rise/Run=4/5 The slope of the line is 45. Now we are ready to write the complete equation. y= 4/5x+ 1 Finally, we can substitute x=3 into this equation and predict the corresponding y-value.
   y=4/5x+1

   Substitute

   x= 3

   y=4/5( 3)+1

   ▼

   Simplify right-hand side

   MoveRightFacToNum

   a/c* b = a* b/c

   y=4*3/5+1

   Multiply

   Multiply

   y=12/5+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.