Exercise 7 Page 366

y=x+4

We can calculate the predicted values for y=x+4.

Now we can calculate the residuals which are the differences between the actual values and the predicted values.

Now, we will square the residuals and find their sum s. This sum will represent how good the fit is. The lower the sum, the better fit. Let's do it!

We found that the sum for y=x+4 is s=7. Let's repeat this process for y=x+4.2.

y=x+4.2

Let's find the predicted values and the residuals for y=x+4.2.

Now, we will square the residuals and find the sum s for the line y=x+4.2.

We found that the sum s for y=4.2 is equal to 7.56.

Comparison

We found that the sum of the squared residuals for y=x+4.2 is 7.56 and that the sum for y=x+4 is 7. As a result, we can say that y=x+4 is the better line of fit because it has lesser sum.