Question

for the line of fit p = -26t + 5,649 , where t is the number of years since 1990 , what is the residual of the data point at t = 5?

Answer 1

According to the problem, the equation of the line that best fit is

`p=-26t+5649`

To find the population when t = 5, we just have to evaluate the expression.

`\begin{gathered} p=-26\cdot5+5649=-130+5649 \\ p=5519 \end{gathered}`

Note that this value (p=5519) is different from the value assigned in the given table. In this way, the residual refers to the difference between these values.

`r=5530-5519=11`

It's important to know that the residual r=11 is positive because the value shown in the table (empirical data) is greater than the resulting value from the equation.

Therefore, the residual is 11.