finding the relationship between x and y values

[resqswmr2]

Use a scatter plot to determine the relationship between the x values and the y values

x__7___2___4___5___1___6___3__
y__5__26___20__15__30__12__25_

Is it:
-Negative linear relationship
-Nonlinear relationship
-No relationship
-Positive linear relationship

This is the only one I can't figure out. Can someone help?

 

[Mrspi]

Use a scatter plot to determine the relationship between the x values and the y values

x__7___2___4___5___1___6___3__
y__5__26___20__15__30__12__25_

Is it:
-Negative linear relationship
-Nonlinear relationship
-No relationship
-Positive linear relationship

This is the only one I can't figure out. Can someone help?

Did you actually use graph paper and PLOT the points?

 

[soroban]

Hello, resqswmr2!

Use a scatter plot to determine the relationship between the \(\displaystyle x\) values and the \(\displaystyle y\) values

. . \(\displaystyle \begin{array}{c||c|c|c|c|c|c|c} x &7&2&4&5&1&6&3 \\ \hline y&5&26&20&15&30&12&25 \end{array}\)

Is it:
. . (a) Negative linear relationship
. . (b) Positive linear relationship
. . (c) Nonlinear relationship
. . (d) No relationship

This is the only one I can't figure out. . How did you figure out the other ones?

First, I'd write those points in order . . .

. . . \(\displaystyle \begin{array}{c||c|c|c|c|c|c|c} x&1&2&3&4&5&6&7 \\ \hline y&30&26&25&20&15&12&5 \end{array}\)

We see that, as \(\displaystyle x\) increases, \(\displaystyle y\) decreases.
. . I'd say that there is a relationship.


Take differences of consecutive y-values.

. . \(\displaystyle \begin{array}{cccccccccccccc}y\text{-values} & 30 && 26 && 25 && 20 && 15 && 12 && 5 \\ \text{di{f}ferences} && \text{-}4 && \text{-}1 && \text{-}5 && \text{-}5 && \text{-}3 && \text{-}7 \end{array}\)

We see that the differences are not constant . . . The relationship is not linear.

(If you had graphed the points like they suggested,
. . you'd see that they do not form a straight line.}


I would say it is: .(c) Nonlinear relationship.

 

[fasteddie65]

On the other hand, I would say "negative linear relationship" because you can draw a line going through the data, and it would have a negative slope. You could even do a linear regression on the data; I get the equation y = -4.036x + 35.143 as the line of best fit.