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# Math Bellevue Essay

5441 words - 22 pages

1. | What is the slope of the regression line? |
The slope is the coefficient before the x variable (D in this case). Thus the answer is 0.0138.
| Points Earned: | 1/1 |
| A. | If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water. |
B. | If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water. |
C. | If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water. |
|
In the ...view middle of the document...

A typical regression equation for water entering a municipal treatment plant isBOD = −55.43 + 1.507 TOCBoth BOD and TOC are measured in milligrams per liter of water. |

5. | What does the slope of this line say about the relationship between BOD and TOC? |
| A. | For every unit increase in BOD, the TOC increases by 1.507 units. |
B. | For every unit increase in TOC, the BOD increases by 1.507 units. |
C. | For every unit increase in TOC, the BOD decreases by 1.507 units. |
D. | For every unit increase in TOC, the BOD decreases by -55.34 units. |
|
The slope of the line measures the rate of increase/decrease of the y variable for a change of one unit in the x variable.
| Points Earned: | 1/1 |
6. | What is the predicted BOD when TOC = 1? Give your answer up to three decimal places. |
The predicted value of the BOD at TOC = 1 is given by the regression equation ŷ = −55.43 + 1.507 x = −55.43 + 1.507 × 1 = −53.923
| Points Earned: | 1/1 |
| Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirect—a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its “absorbence.” To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbence and pollutant concentration. This is usually done every day. Here is one series of data on the absorbence for different levels of nitrates. Nitrates are measured in milligrams per liter of water.

Data Set |

7. | Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997, something went wrong and the calibration procedure is repeated. Plot the data and ﬁnd the correlation. Must the calibration be done again? |
| A. | Yes |
B. | No |
|
Using a calculator or spreadsheet we find the correlation to be 0.999939232, thus there is no need to repeat the experiment.
| Points Earned: | 1/1 |
8. | The calibration process sets nitrate level and measures absorbence. Once established, the linear relationship will be used to estimate the nitrate level in water from a measurement of absorbence. What is the equation of the line used for estimation? |
| A. | ŷ = −8.8250 − 14.5271x |
B. | ŷ = −14.5217 + 8.8250x |
C. | ŷ = 1.333 − .1657x |
D. | ŷ = 14.522 + 8.825x |
|
Using the spreadsheet or calculator we find that the slope is given by b = 8.8250, while the intercept is a = −-14.5217 Thus the equation that matches ŷ = a + bx.
| Points Earned: | 1/1 |
9. | Based on the equation exactly as it appears in your choice in the previous question (to avoid roundoff errors), what is the estimated nitrate level in a...

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