Question

A research company is looking at the correlation between the years since 1970 and the average amount of years that couples stay married. Use complete sentences to explain how the data below indicates a non-linear model.


Time (in years) since 1970: 0, 10, 20, 30, 40
Average age of a marriage (yrs.): 10, 11.2, 13.9, 17.2, 29

Answer 1

Answer and Step-by-step explanation:

Since we have given that

Time                Average age of a marriage

0                                  10

10                                 11.2

20                                13.9

30                                17.2

40                                29

We need to show that the above data indicated a non linear model.

For this it is enough to show that slope is different:

So, we consider the slope for first 2 points:

(0,10) and (10,11.2)

So, slope becomes

$m_1=\dfrac{y_2y_1}{x_2-x_1}=\dfrac{11.2-10}{10-0}=\dfrac{1.2}{10}=0.12$

and similarly, (10,11.2) and (20,13.9)

$m_2=\dfrac{y_2-y_}{x_2-x_1}\\m_2=\dfra{13.9-11.2}{20-10}=\dfrac{2.7}{10}=0.27$

so, $m_1\neq m_2$

So, it becomes non linear model.