medium · SAT Math
A city water utility recorded average daily temperature (x, in degrees Fahrenheit) and daily water usage (y, in thousands of gallons) for a residential zone over 6 days. The scatterplot data are: x = 60, y = 110; x = 65, y = 118; x = 70, y = 127; x = 75, y = 135; x = 80, y = 142; x = 85, y = 150. The line of best fit is y = 1.6x + 14, where x is average daily temperature in degrees Fahrenheit and y is daily water usage in thousands of gallons. On a day when the temperature reached 95°F, the actual measured usage was 158 thousand gallons.
Does the line of best fit over-predict or under-predict usage on this day, and by how much?
- The line under-predicts usage by 8 thousand gallons because the residual is 158 - 166 = -8.
- The line over-predicts usage by 8 thousand gallons because the residual is 158 - 166 = -8.
- The line over-predicts usage by 166 thousand gallons because the predicted value is 166.
- The line under-predicts usage by 8 thousand gallons because the residual is 166 - 158 = 8.
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