Question

observation with smallest residual =
observation with largest residual =

Explanation:

Step1: Understand Residual Concept

Residual is the vertical distance between a data point and the regression line. Smallest residual means the point is closest to the line; largest residual means the point is farthest (either above or below).

Step2: Analyze Each Point

• For the point at \( x = 12 \) (approx), \( y \approx 7 \): Check distance to the line. The line at \( x = 12 \) has \( y \approx 7 \) (since the line passes near here), so residual is small.
• For the point at \( x = 25 \), \( y \approx 28 \): The line at \( x = 25 \) has \( y \approx 20 \) (from the line's slope), so vertical distance is large (above the line).
• Other points: Compare distances. The point around \( x = 12, y = 7 \) is closest to the line (smallest residual). The point at \( x = 25, y = 28 \) is farthest (largest residual).

Answer:

Observation with smallest residual = The point around (12, 7) (or the middle - left point near the line)
Observation with largest residual = The top - most point at (25, 28)

(Note: Based on the graph, the point with \( x\approx12, y\approx7 \) is closest to the line (smallest residual), and the point at \( x = 25, y = 28 \) is farthest above the line (largest residual).)