Two students have examined the scatter plot shown and made statements regarding their analysis of the data.

Question

Graph- (23,0) (23,1) (19,2) (19,3) (17,4) (14,5) (14,6) (11,7) (8,8) (8,9) (5,10)

Student A claims that there is a negative association that would be non-linear. The dependent variable is the amount in the account and the independent variable is the month. 

Student B claims that there is a positive association that would be linear. The dependent variable is the month and the independent variable is the amount in the account.

Neither student is fully correct.

Create a set of claim statements (sentences) that would be 100% correct.

1 sentence should include vocabulary about the type of associations visible in the data (see Student A and Student B first sentence)

1 sentence should include vocabulary about the variables (see Student A and Student B last sentence)

Answer 1

First plot the data as given with the amount in the account as the independent variable (x-axis). Use your graphing calculator or a graphing app such as desmos.com or geogebra; or just use a piece of graph paper. You will get a clear negative association that is linear. So student A was incorrect in saying it was non-linear.

Second, plot the data again using the month as the independent variable (x-axis). Once again, you will get a clear negative correlation that is linear. So student B was incorrect in saying it was a positive association.

Typically, the month is the independent variable, and the amount in the account would be the dependent variable. The correlation is negative and linear.

Answer 2

First Principles without relying on software says,.

linear means that the growth or decay is constant

one unit to the next unit of independent variable.

let independent variable be month.

from one month to the next

(23,0) (23,1) (19,2) (19,3) (17,4) (14,5) (14,6) (11,7) (8,8) (8,9) (5,10)

the decline is 0,4,0,2,3.0,3,3,0,3

which is not constant. A true linear relationship would have an equation

something like A=23-2x where A is amount and x is month

then decline would be 2,2,2,2,2,2,2,2,2,2,2

and that is linear, or arithmetic decline.