Question

make a residual plot for the linear model and the data set it represents. how well does the model fit the data set?
y = -0.06x + 12.2
x | y
10 | 9
15 | 13
20 | 13
25 | 12
30 | 8
choose the correct residual plot below
a.
plot a
b.
plot b
c.
plot c
d.
plot d
the points in the residual plot seem to be randomly distributed on either side of the x - axis, and they dropdown clustered fairly close to the x - axis. the model dropdown the data set well.

Explanation:

Step1: Calculate Residuals

Residual \( r = y_{\text{actual}} - y_{\text{predicted}} \). For each \( x \), compute \( y_{\text{predicted}} = -0.06x + 12.2 \), then residual.

• \( x = 10 \): \( y_{\text{pred}} = -0.06(10) + 12.2 = 11.6 \), \( r = 9 - 11.6 = -2.6 \)
• \( x = 15 \): \( y_{\text{pred}} = -0.06(15) + 12.2 = 11.3 \), \( r = 13 - 11.3 = 1.7 \)
• \( x = 20 \): \( y_{\text{pred}} = -0.06(20) + 12.2 = 11.0 \), \( r = 13 - 11.0 = 2.0 \)
• \( x = 25 \): \( y_{\text{pred}} = -0.06(25) + 12.2 = 10.7 \), \( r = 12 - 10.7 = 1.3 \)
• \( x = 30 \): \( y_{\text{pred}} = -0.06(30) + 12.2 = 10.4 \), \( r = 8 - 10.4 = -2.4 \)

Step2: Match Residual Plot

Residuals: \( -2.6, 1.7, 2.0, 1.3, -2.4 \). Plotting these (x: 10,15,20,25,30; y: residuals) should match Option B (residuals: lower at x=10,30; higher at x=15,20,25, random around x-axis, close to x-axis).

Step3: Analyze Fit

Residuals are randomly distributed (no pattern) and close to x-axis, so model fits well.

Answer:

Correct residual plot: B. The points seem to be randomly distributed, are clustered close to the x - axis, and the model fits the data set well.