Least-Squares Line, Prediction & Extrapolation (Grade 11)
Free printable Grade 11 General Mathematics worksheet: fit a least-squares line, make predictions, and distinguish interpolation from extrapolation (ACMGM057, ACMGM062).
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Grade 11 · Math worksheet
Name
Date
Math
Bivariate Data: Least-Squares Line, Prediction & Extrapolation (Year 11-12 General Mathematics)
Fit a least-squares line y = a + bx to each data set, use it to make predictions, classify each prediction as interpolation or extrapolation, and interpret the slope. Coefficients and predictions are computed from the data.
- 1.For hours spent studying (x, hours) and exam mark (y, %): (1, 56), (2, 52), (3, 67), (4, 71), (5, 76), (6, 85). Find the equation of the least-squares line in the form y = a + bx (a and b to 2 decimal places).
- 2.Using the least-squares line y = 45.73 + 6.31x, predict y when x = 3, and state whether this is interpolation or extrapolation (the data ranges from x = 1 to x = 6). Give the prediction to 1 decimal place.
- 3.Using the same line y = 45.73 + 6.31x, predict y when x = 10, and state whether this is interpolation or extrapolation. Give the prediction to 1 decimal place, and note the reliability of this prediction.
- 4.Interpret the slope of the least-squares line y = 45.73 + 6.31x in the context of exam mark and hours spent studying.
- 5.For hours of TV watched per day (x, hours) and test score (y, %): (0, 80), (1, 73), (2, 67), (3, 71), (4, 56). Find the equation of the least-squares line in the form y = a + bx (a and b to 2 decimal places).
- 6.Using the least-squares line y = 79.4 - 5x, predict y when x = 1, and state whether this is interpolation or extrapolation (the data ranges from x = 0 to x = 4). Give the prediction to 1 decimal place.
- 7.Using the same line y = 79.4 - 5x, predict y when x = 7, and state whether this is interpolation or extrapolation. Give the prediction to 1 decimal place, and note the reliability of this prediction.
- 8.Interpret the slope of the least-squares line y = 79.4 - 5x in the context of test score and hours of TV watched per day.
- 9.For age of the car (x, years) and resale value (y, $000): (1, 28), (2, 23), (3, 25), (4, 21), (5, 18). Find the equation of the least-squares line in the form y = a + bx (a and b to 2 decimal places).
- 10.Using the least-squares line y = 29.6 - 2.2x, predict y when x = 2, and state whether this is interpolation or extrapolation (the data ranges from x = 1 to x = 5). Give the prediction to 1 decimal place.
- 11.Using the same line y = 29.6 - 2.2x, predict y when x = 8, and state whether this is interpolation or extrapolation. Give the prediction to 1 decimal place, and note the reliability of this prediction.
- 12.Interpret the slope of the least-squares line y = 29.6 - 2.2x in the context of resale value and age of the car.
- 13.For fertiliser applied (x, kg) and crop yield (y, tonnes): (1, 10), (2, 20), (3, 24), (4, 23), (5, 30). Find the equation of the least-squares line in the form y = a + bx (a and b to 2 decimal places).
- 14.Using the least-squares line y = 8.5 + 4.3x, predict y when x = 4, and state whether this is interpolation or extrapolation (the data ranges from x = 1 to x = 5). Give the prediction to 1 decimal place.
- 15.Using the same line y = 8.5 + 4.3x, predict y when x = 8, and state whether this is interpolation or extrapolation. Give the prediction to 1 decimal place, and note the reliability of this prediction.
- 16.Interpret the slope of the least-squares line y = 8.5 + 4.3x in the context of crop yield and fertiliser applied.
- 17.For hours of exercise per week (x, hours) and resting heart rate (y, bpm): (0, 80), (1, 80), (2, 80), (3, 69), (4, 68). Find the equation of the least-squares line in the form y = a + bx (a and b to 2 decimal places).
- 18.Using the least-squares line y = 82.4 - 3.5x, predict y when x = 2, and state whether this is interpolation or extrapolation (the data ranges from x = 0 to x = 4). Give the prediction to 1 decimal place.
- 19.Using the same line y = 82.4 - 3.5x, predict y when x = 7, and state whether this is interpolation or extrapolation. Give the prediction to 1 decimal place, and note the reliability of this prediction.
- 20.Interpret the slope of the least-squares line y = 82.4 - 3.5x in the context of resting heart rate and hours of exercise per week.
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