Least-Squares Line, Prediction & Extrapolation (Grade 12)
Free printable Grade 12 General Mathematics worksheet: fit a least-squares line, make predictions, and distinguish interpolation from extrapolation (ACMGM057, ACMGM062).
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Grade 12 · 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, 46), (2, 55), (3, 61), (4, 68), (5, 74), (6, 84). 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 = 39.27 + 7.26x, predict y when x = 5, 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 = 39.27 + 7.26x, 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 = 39.27 + 7.26x 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, 88), (1, 80), (2, 77), (3, 63), (4, 56), (5, 53). 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 = 88.14 - 7.46x, predict y when x = 1, and state whether this is interpolation or extrapolation (the data ranges from x = 0 to x = 5). Give the prediction to 1 decimal place.
- 7.Using the same line y = 88.14 - 7.46x, predict y when x = 9, 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 = 88.14 - 7.46x 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, 32), (2, 28), (3, 20), (4, 23), (5, 14), (6, 16). 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 = 34.07 - 3.4x, 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.
- 11.Using the same line y = 34.07 - 3.4x, 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.
- 12.Interpret the slope of the least-squares line y = 34.07 - 3.4x in the context of resale value and age of the car.
- 13.For fertiliser applied (x, kg) and crop yield (y, tonnes): (1, 16), (2, 19), (3, 23), (4, 22), (5, 27), (6, 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 = 13.53 + 2.66x, predict y when x = 5, and state whether this is interpolation or extrapolation (the data ranges from x = 1 to x = 6). Give the prediction to 1 decimal place.
- 15.Using the same line y = 13.53 + 2.66x, 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 = 13.53 + 2.66x 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, 82), (1, 76), (2, 75), (3, 72), (4, 73). 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 = 80 - 2.2x, 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 = 80 - 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.
- 20.Interpret the slope of the least-squares line y = 80 - 2.2x in the context of resting heart rate and hours of exercise per week.
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