Algebra U13 HW DAY 6 REGRESSION EQUATIONS

1. The time spent in surgery and the cost of surgery was recorded for six patients. The results and scatter plot are shown below.

  1. Calculate the equation of the least-squares line (regression equation), rounding all coefficients to the nearest hundredth.
  1. Draw the least-squares line on the graph above. (Hint: Substitute x = 30 into your equation to find the predicted y-value. Plot the point (30, your answer) on the graph. Then substitute x = 180 into the equation and plot the point. Join the two points with a straightedge.)
  1. What does the least-squares line predict for the cost of a surgery that lasts 118 minutes? (Calculate the cost to the nearest cent.)
  1. What is the difference between the answer to question (c) and the actual cost of a surgery lasting 118 minutes? ACTUAL – PREDICTED = RESIDUAL
  1. Show your answer to question (d) as a vertical line between the point for that person in the scatter plot and the least-squares line.

2.The table shows how wind affects a runner’s performance in the 200 meter dash. Positive wind speeds correspond to tailwinds, and negative wind speeds correspond to headwinds. The change, t, in finishing time is the difference between the runner’s time when the wind speed is s and the runner’s time when there is no wind.

Wind speed (m/sec), s / -6 / -4 / -2 / 0 / 2 / 4 / 6
Change in finishing time (sec), t / 2.28 / 1.42 / 0.67 / 0 / -0.57 / -1.05 / -1.51

Write the equation of the quadratic regression model, rounding to the nearest hundredth.

Predict the change in finishing time when the wind speed is 10 m/sec.

Hours since observation began / Number of bacteria in the sample
0 / 20
1 / 40
2 / 75
3 / 150
4 / 297
5 / 510

3.A rapidly growing bacteria has been discovered. Its growth rate is shown in the chart. Write the exponential regression model for this data,

rounding to the nearest thousandth.

Using your regression equation, determine how many bacteria, to the nearest integer, will be present in 3.5 hours.

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