Question

choose the correct residual plot below.
a.
y
3
2
1
0
-1
-2
-3
x
10 20 30 40
b.
y
3
2
1
0
-1
-2
-3
x
10 20 30 40
c.
y
3
2
1
0
-1
-2
-3
x
10 20 30 40
d.
y
3
2
1
0
-1
-2
-3
x
10 20 30 40
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: Recall Residual Plot Criteria

A good residual plot (for a well - fitting model) has points randomly distributed around the x - axis, with no obvious pattern (like a curve, cluster with a trend). Also, points should be relatively close to the x - axis.

Step2: Analyze Each Option

• Option A: The points seem to have a pattern (upper points at x = 10,20,30 and lower points at x = 10,20,30) with a sort of symmetric but non - random distribution.
• Option B: The points are randomly distributed above and below the x - axis, and they are relatively close to the x - axis. There is no obvious pattern (like a curve or a trend in the residuals).
• Option C: The points have a pattern (upper points at x = 10,20,30 and lower points at x = 20,30) which is not random.
• Option D: The points have a pattern (upper points at x = 10,30 and lower points at x = 20,30) which is not random.

Answer:

B. The graph for option B