I\'m off by a few decimal points.. Keeping water supplies clean requires regular
ID: 3209357 • Letter: I
Question
I'm off by a few decimal points..
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. 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. (Do this on paper. Your instructor may ask you to turn in this work.) Find the correlation. (Use 4 decimal places.) r = Must the calibration be done again? The calibration process sets nitrate level and measures absorbence. Once establishes 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? (Use 2 decimal places for intercept and 3 decimal places for slope.) cap y = + What is the estimated nitrate level in a water specimen with absorbence 42? (Use 1 decimal place.) mg/l Do you expect estimates of nitrate level from absorbence to be quite accurate? Why? This prediction is of a value that is not in the range of the data and therefore cannot be accurate. Since the calibration is so important, it is Inaccurate to use this regression to predict. This prediction should be very inaccurate because the relationship is too perfectly linear. This prediction should be very accurate because the relationship is so strong as indicated by r.Explanation / Answer
Solution:
Here, we have to use the regression analysis for answering the questions. The regression model for the given data for dependent variable Nitrates and independent variable absorbance is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.999962007
R Square
0.999924016
Adjusted R Square
0.999914518
Standard Error
7.421503808
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
5798559.37
5798559.4
105277.6735
9.11495E-18
Residual
8
440.6297502
55.078719
Total
9
5799000
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-14.25820686
3.52698289
-4.0426073
0.003722235
-22.39144398
-6.124969742
Absorbance X
8.84050716
0.027246395
324.46521
9.11495E-18
8.777676862
8.903337458
Part a
The correlation coefficient between the dependent variable and independent variable is given as below:
r = 1.0000 (Rounded to four decimal places)
Must the calibration be done again?
No
(Because r > 0.997)
Part b
The regression equation is given as below:
Y = -14.26 + 8.841*X
Now, we have to compute the estimate for nitrate when absorbance = 42
Y = -14.26 + 8.841*42 = 357.062
Y = 357.1 (rounded to one decimal places)
Part c
Do you expect estimates of nitrate level from absorbance to be quite accurate? Why?
Answer:
This prediction should be very accurate because the relationship is so strong as indicated by r.
(r is very strong, r = 1.0000 approximately)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.999962007
R Square
0.999924016
Adjusted R Square
0.999914518
Standard Error
7.421503808
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
5798559.37
5798559.4
105277.6735
9.11495E-18
Residual
8
440.6297502
55.078719
Total
9
5799000
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-14.25820686
3.52698289
-4.0426073
0.003722235
-22.39144398
-6.124969742
Absorbance X
8.84050716
0.027246395
324.46521
9.11495E-18
8.777676862
8.903337458