A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of ...
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Find the correlation coefficient & interpret it. Find & interpret the slope. PowerPoint PPT Presentation


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A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. Find the correlation coefficient & interpret it. Find & interpret the slope. Find & interpret the y-intercept. Give the least squares regression line.

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Find the correlation coefficient & interpret it. Find & interpret the slope.

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A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient.

  • Find the correlation coefficient & interpret it.

  • Find & interpret the slope.

  • Find & interpret the y-intercept.

  • Give the least squares regression line.


A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient.

  • Find the correlation coefficient & interpret it.

  • Find & interpret the slope.

    • For every additional mg the heart rate decreases by 38.56 bpm.

  • Find & interpret the y-intercept.

  • Write LSRL:


Residuals

Section 3.2B


Residuals

  • Variation in the y values can be effectively explained when the residuals are small – close to the line.

  • Remember a residual = observed – exp.


The equation to explain the relationship between drug dosage and heart rate is shown below.

Find the predicted value for a dosage of 0.4 mg.

Find the residual for (0.4, 80).


The equation to explain the relationship between drug dosage and heart rate is shown below.Find the residuals for each value.

* The sum of the residuals is always zero!


Residual Plot

  • It is a scatterplot of the residuals vs the explanatory variable.

  • They help us to assess how well a regression line fits the data.

  • The residual plot should show no obvious pattern

  • The residuals should be relatively small.


The equation to explain the relationship between drug dosage and heart rate is shown below.Graph the residual Plot. Is the linear model appropriate?

* The sum of the residuals is always zero!


Residual Plot


Height vs Shoe size – residual plot

Good residual plot – show relatively no pattern.


Good or Bad


Standard Deviation of the Residuals

  • It represents the approximate size of a “typical” or “average prediction error (residual).

  • Formula:


The equation to explain the relationship between drug dosage and heart rate is shown below.Find the standard deviation of the residuals.


Homework

*Page 191 (43, 45, 55, 60, 62)


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