# 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!

### Height vs Shoe size – residual plot

Good residual plot – show relatively no pattern.

### Standard Deviation of the Residuals

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

• Formula:

### Homework

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