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

Dosage Heart rate

0.125 95

0.2 90

0.25 93

0.3 92

0.35 88

0.4 80

0.5 82

1. Find the correlation coefficient & interpret it.

2. Find & interpret the slope.

3. Find & interpret the y-intercept.

4. 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.

Dosage Heart rate

0.125 95

0.2 90

0.25 93

0.3 92

0.35 88

0.4 80

0.5 82

1. Find the correlation coefficient & interpret it.

2. Find & interpret the slope.

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

3. Find & interpret the y-intercept.

4. Write LSRL:

RESIDUALSSection 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.

Dosage Heart rate

0.125 95

0.2 90

0.25 93

0.3 92

0.35 88

0.4 80

0.5 82

1. Find the predicted value for a dosage of 0.4 mg.

2. 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.

Dosage Heart rate

0.125 95

0.2 90

0.25 93

0.3 92

0.35 88

0.4 80

0.5 82

* 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. Find the residuals for each value.

Dosage Heart rate

0.125 95 95.47 -0.47

0.2 90 92.58 -2.578

0.25 93 90.65 2.35

0.3 92 88.72 3.278

0.35 88 86.79 1.206

0.4 80 84.87 -4.866

0.5 82 81.01 0.99

* The sum of the residuals is always zero!

Residual Plot

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

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-5

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Dosage Residual Plot

Dosage

Res

idu

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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.

Dosage Heart rate

0.125 95 95.47 -0.47 0.2209

0.2 90 92.59 -2.578 6.6461

0.25 93 90.65 2.35 5.5225

0.3 92 88.72 3.278 10.745

0.35 88 86.79 1.206 1.4544

0.4 80 84.87 -4.866 23.678

0.5 82 81.01 0.99 0.9801

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Homework

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