Fitting Lines to Data - Pre Algebra

1. What is extrapolation, and why is it risky?

   Using a trend line to predict far outside the range of the data. The trend may not continue there.

2. The trend line $y = -1.5x + 40$ models liters of water $y$ left in a tank after $x$ hours. By how much does the predicted amount drop in 4 hours?

   6 liters. The slope means a drop of 1.5 liters per hour, and $1.5 \times 4 = 6$.

3. When is a straight trend line a poor model for a scatter plot?

   When the association is nonlinear (curved) or there is no association, a straight line does not describe the data well.

4. What does the trend line $y = 0.5x + 2$ predict for $y$ when $x = 10$?

   $7$. $0.5(10) + 2 = 7$.

5. The trend line $y = 3x + 50$ predicts a test score $y$ from hours studied $x$. What score does it predict for 4 hours?

   62. $3(4) + 50 = 62$.

6. The trend line $y = 3x + 50$ predicts a test score $y$ from hours studied $x$. What does the slope 3 mean?

   Each additional hour of study is associated with a predicted increase of about 3 points.

7. The trend line $y = 3x + 50$ predicts a test score $y$ from hours studied $x$. What does the $y$-intercept 50 mean?

   The predicted score for a student who studies 0 hours is 50.

8. What does a trend line with a negative slope tell you about the data?

   There is a negative association: as $x$ increases, $y$ tends to decrease.

9. What is a trend line (line of best fit) on a scatter plot?

   A straight line that models the overall trend of the data, passing close to as many points as possible.

10. A trend line passes through $(0, 10)$ and $(5, 30)$. What is its equation?

    $y = 4x + 10$. The slope is $\frac{30 - 10}{5 - 0} = 4$, and the $y$-intercept is 10.

11. A trend line predicts 62 at $x = 4$, but the actual data point is $(4, 58)$. Is the point above or below the line?

    Below the line. The actual value 58 is less than the predicted value 62.

12. When fitting a trend line informally, how should the data points fall around it?

    Close to the line, with roughly as many points above it as below it.

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