Regression Analysis: Linear & Quadratic Models
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Excel (Regression)
The dataset mercury.xls has two variables both numeric:
- methyl mercury intake (INTAKE)
- mercury in whole blood (BLOOD)
These two measures were recorded on a sample of 15 subjects exposed to methyl mercury through consumption of contaminated fish. The researcher wants to know if is possible to predict the level of mercury in the blood from the level of mercury intake.
a. Identify the dependent (Y) and the independent (X) variables
b. Plot the data and comment of the relationship between X and Y
c. Determine the LSE estimates of the slope (b1) and the intercept (b0)
d. Test for the null hypothesis that b1=0 and interpret the results.
e. Can you suggest a model that would describe the relationship between Blood and Intake better than the straight line model?
Data set
INTAKE BLOOD
180 90
200 120
230 125
410 290
600 310
550 290
275 170
580 375
105 70
250 105
460 205
650 480
350 195
280 160
420 210
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Solution Summary
The solution provides step by step method for the calculation of regression analysis. Formula for the calculation and Interpretations of the results are also included.
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Excel (Regression)
The dataset mercury.xls has two variables both numeric:
- Methyl mercury intake (INTAKE)
- Mercury in whole blood (BLOOD)
These two measures were recorded on a sample of 15 subjects exposed to methyl mercury through consumption of contaminated fish. The researcher wants to know if is possible to predict the level of mercury in the blood from the level of mercury intake.
Answers
a. Identify the dependent (Y) and the independent (X) variables
Dependent variable, Y - BLOOD
Independent variable, X - INTAKE
b. Plot the data and comment of the relationship between X and Y
In the scatter plot the points are closely clustered around the regression line. Hence there is a strong relationship exists between X and Y. Also the level of mercury in the blood increases as the level of mercury intake increases. That is, there is a positive relationship exists between X and Y.
Thus there is a strong positive relationship exists between X and Y.
c. ...
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