Question

make a residual plot for the linear model and the data set it represents. how well does the model fit the data set?

choose the correct residual plot below.

the points in the residual plot

to be randomly distributed on either side of
the x - axis, and they

clustered fairly close to the x - axis. the model

the data set well.

Explanation:

Step1: Calculate residuals

Residual = Observed \( y - \) Predicted \( y \).
For \( x = 10 \), predicted \( y=-0.54\times10 + 21.4=16 \), residual \( = 16 - 16=0 \).
For \( x = 15 \), predicted \( y=-0.54\times15 + 21.4 = 13.3 \), residual \( = 13 - 13.3=-0.3 \).
For \( x = 20 \), predicted \( y=-0.54\times20+21.4 = 10.6 \), residual \( = 11 - 10.6 = 0.4 \).
For \( x = 25 \), predicted \( y=-0.54\times25+21.4 = 7.9 \), residual \( = 8 - 7.9 = 0.1 \).
For \( x = 30 \), predicted \( y=-0.54\times30+21.4 = 5.2 \), residual \( = 5 - 5.2=-0.2 \).

Step2: Analyze residual plot

Residuals should be randomly distributed around the \( x - \) axis for a good - fit model.
When \( x = 10 \), residual \( = 0 \); \( x = 15 \), residual \(=-0.3 \); \( x = 20 \), residual \( = 0.4 \); \( x = 25 \), residual \( = 0.1 \); \( x = 30 \), residual \(=-0.2 \).
Plotting these points, we can see that the points in the residual plot are randomly distributed on either side of the \( x - \) axis.

Answer:

The points in the residual plot are randomly distributed on either side of the \( x - \) axis. The model fits the data set well.