Question

etermine which scatter plots suggest a linear relationship between x and y.(4 points)
Linear relationship NOT a linear relationship












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Answer 1

I don’t see the four scatter plots — please upload them or describe each (rough shape/trend of the points). Meanwhile, here’s a quick checklist and simple tests you can use to decide which plots show a linear relationship:

Visual rules
- Linear relationship: the points lie roughly along a straight line (either sloping up = positive or down = negative). Points may scatter a bit around the line but show a clear single straight-line trend.
- NOT linear: the points form a curved pattern (U-shaped, exponential, etc.), form distinct clusters with no single line through them, or look like a random cloud with no trend.

Quick statistical checks
- Compute the correlation coefficient r. If |r| is large (e.g., > 0.7) there is a strong linear relationship; if |r| is near 0 (e.g., < 0.3) there is little or no linear relationship.
- Fit a least-squares line and inspect residuals: if residuals are small and randomly scattered around zero, the linear model fits well; clear systematic residual patterns (curvature) mean the relationship is not linear.
- R-squared (R^2) gives the proportion of y-variation explained by the linear model; higher R^2 indicates a better linear fit.

Examples
- Points clustered tightly along an upward sloping line → Linear.
- Points in a U shape or exponential curve → NOT linear.
- Points randomly scattered with no trend → NOT linear.
- Points scattered roughly along a line but with some spread → Linear (possibly moderate).

If you upload the four plots or describe each one briefly (e.g., “points slope up tightly,” “U-shaped,” “random cloud,” “two separate clusters”), I’ll sort them into “Linear” vs “NOT a linear relationship” for you.