Mississippi Math FA.S.44
The Standard
Justify the relationship between the correlation coefficient and the rate of change for the line of best fit.
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students explain why the correlation coefficient and the slope of a best-fit line have the same sign. They use the spread of the x-values and y-values to explain why the two numbers are usually different.
What Mastery Looks Like
- Given r = 0.8, an x standard deviation of 2, and a y standard deviation of 10, a student finds a slope of 4. They explain that multiplying every y-value by 10 multiplies the slope by 10 but leaves r unchanged.
Common Misconceptions
- Students may use r as the slope or assume a steeper line means a stronger correlation. They may also think changing units changes r, even though it changes the slope.
How to Assess It
- Exit ticket: A data set has r = 0.6, an x standard deviation of 2, and a y standard deviation of 10. Find the slope, then explain what happens to the slope and r if every y-value doubles.
Lesson moves
Ways to Teach It
Enter (1,2), (2,4), (3,5), (4,7), and (5,9) in a spreadsheet, graph them, then multiply every y-value by 10 and compare slopes and r.
Ask: If two data sets both have r = 0.8, must their best-fit lines have equal slopes? Explain using the spreads of x and y.
Hand out cards showing r and the x and y standard deviations; students calculate each slope and match it to a slope card.
Compare weekly training miles with race time, then convert miles to kilometers and explain why r stays fixed while the slope changes.
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Related Standards
- FA.S.43
For scatter plots that suggest a linear association, informally fit a straight line and predict the equation for the line of best fit. (8.SP.2)
- FA.F.15
Determine the rate of change of a linear function from a description of a relationship or from two (x, y) values, including reading these from a table or from a...
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