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TexasMathsSyllabus dot point

How do you analyze a scatterplot, write a trend line, judge correlation, and use the model to make predictions?

Use scatterplots to analyze the relationship between two quantitative variables, write a trend-line equation by informal methods, judge its reasonableness, and make predictions, interpreting the correlation (TEKS A.3F, A.3G, A.4A, A.4B, A.4C).

A STAAR Algebra I answer on scatterplots, writing a trend line, correlation (positive, negative, none, and the correlation coefficient r), and making predictions (TEKS A.3F, A.3G, A.4A, A.4B, A.4C).

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  1. What this topic is asking
  2. Reading a scatterplot
  3. Direction and strength of correlation
  4. Writing a trend line and predicting
  5. Interpreting and judging reasonableness
  6. How STAAR examines this topic
  7. Try this

What this topic is asking

Two-variable data rounds out Reporting Category 2. TEKS A.3F, A.3G, and A.4 ask you to read a scatterplot, write a trend line (line of best fit) by informal methods, judge its reasonableness, describe the correlation (including the correlation coefficient rr), and use the model to predict. On STAAR this is mostly multiple choice and equation-editor work, with the calculator available to find a regression line.

Reading a scatterplot

A scatterplot shows each data pair as a point. Look first for an overall shape: a roughly straight rising or falling band suggests a linear relationship, while a curved band suggests something else. STAAR data is usually close enough to linear to fit a trend line.

Direction and strength of correlation

Describe a correlation with two words: a direction and a strength.

  • Direction. Positive when yy tends to increase as xx increases (line rises); negative when yy tends to decrease as xx increases (line falls); none when there is no pattern.
  • Strength. Strong when points lie close to the line; weak when they scatter widely.

The correlation coefficient rr puts a number on this, from −1-1 to 11. Values near +1+1 are strong positive, near −1-1 strong negative, and near 0 indicate little linear relationship. A calculator returns rr along with the regression line.

Writing a trend line and predicting

A trend line balances the points, roughly equal numbers above and below. By informal methods, pick two points the line passes near and use them to find slope and intercept; by calculator, use linear regression.

Interpreting and judging reasonableness

The trend line's slope is a rate (cm per year, dollars per item) and its intercept is the starting value, interpreted exactly as in any linear context. Reasonableness matters: a prediction far outside the data range (extrapolation) can be unrealistic, and a trend line is only meaningful when the points actually follow a linear pattern. Stating whether a prediction makes sense in context is the interpretive credit A.4 rewards.

How STAAR examines this topic

  • Multiple choice. Classify a correlation (direction and strength), or match a scatterplot to a value of rr.
  • Equation editor and number entry. Write a trend-line equation and compute a prediction.
  • Inline choice. Pick positive, negative, or no correlation, and strong or weak, from dropdowns.

A clarifying idea is that correlation is not causation: a strong rr shows the variables move together, not that one causes the other, which is the reasoning caution behind interpreting any data model.

Try this

Q1. Points fall as xx increases, scattered loosely. Describe the correlation. [1 point]

  • Cue. Weak negative.

Q2. A trend line is y=−3x+40y = -3x + 40. Predict yy at x=6x = 6. [1 point]

  • Cue. y=−3(6)+40=22y = -3(6) + 40 = 22.

Exam-style practice questions

Practice questions written in the style of TEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

STAAR (style)1 marksMultiple choice. A scatterplot shows that as the number of hours studied increases, test scores tend to increase, with points lying close to a rising line. Which best describes the correlation? (A) Strong positive (B) Strong negative (C) No correlation (D) Weak negative
Show worked answer →

The correct answer is (A).

As one variable increases the other increases, so the correlation is positive (the trend line rises). Because the points lie close to the line, the relationship is strong. A correlation coefficient rr near +1+1 matches this. Choice (B) would have points falling, and choice (C) would show no pattern. Direction (sign) and strength (how tightly packed) are judged separately.

STAAR (style)2 marksEquation editor. A trend line for a data set passes through (0,50)(0, 50) and (10,90)(10, 90). Write the trend-line equation in slope-intercept form, then predict the value when x=25x = 25.
Show worked answer →

The trend line is y=4x+50y = 4x + 50, and at x=25x = 25 the predicted value is 150150.

Slope =90−5010−0=4010=4= \frac{90 - 50}{10 - 0} = \frac{40}{10} = 4, and the yy-intercept is 50, so y=4x+50y = 4x + 50. Predicting at x=25x = 25: y=4(25)+50=150y = 4(25) + 50 = 150. Using the trend line to estimate beyond the data is extrapolation; STAAR accepts the model's prediction but a reasonableness check (does 150 fit the context?) is the interpretive step the standard rewards.

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