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.

nitrates 50 50 100 200 400 800 1200 1600 2000 2000
absorbence 7.0 7.6 12.7 24.0 47.0 93.0 138.0 183.0 231.0 226.0

the calibration process sets nitrate level and measures absorbence. the linear relationship that results is used to estimate the nitrate level in water from a measurement of absorbence.

a. what is the equation of the line used to estimate nitrate level?
b. what does the slope of this line say about the relationship between nitrate level and absorbence?
c. what is the estimated nitrate level in a water specimen with absorbence 40?

a) Equation is

b) Slope = 0.1135 represents the change in y for a unit change in x

i.e. When nitrate content is increasedby 1, absorbence is increased by 0.1135

Step-by-step explanation:

NitratesAbsorbence

xy

507

507.6

10012.7

20024

40047

80093

1200138

1600183

2000231

2000226

SUMMARY OUTPUT        

Regression Statistics        

Multiple R0.999911043        

R Square0.999822094        

Adjusted R Square0.999799856        

Standard Error1.2890282        

Observations10        

Coefficients

Intercept1.589782721

x0.113500259

we get regression line as

y = 0.1135x+1.590

a) Equation is

b) Slope = 0.1135 represents the change in y for a unit change in x

i.e. When nitrate content is increasedby 1, absorbence is increased by 0.1135

Rigid transformations are ways to move an object while not changing its shape or size. A  

translation (slide) moves . object vertically. horizontally or both. A reflection (flip) moves an object across a line of reflection as in a mirror. A rotation (tum) moves an object clockwise or  

object across a line of reflection as in a mirror. A rotation (tum) moves an object clockwise or  

counterclockwise around s point.

Step-by-step explanation: