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Example 1: Data was collected on the “depth of dive” and the “duration of dive” of "diving birds". The following linear
model was summarised:
d = 0.015+2.915t
where:
• t is the duration of the dive in minutes
• d is the depth of the dive in metres
Interpret the slope and intercept of the regression line in the context of the study.
Solution:
Interpretation of the slope: If the duration of the dive rises by 1 minute, we can estimate that the depth of the dive will
also increase by approximately 2.915 metres.
Interpretation of the intercept: If the duration of the dive is 0 seconds, then we can forecast that the depth of the dive
is 0.015 metres.
Comments: The interpretation of the intercept doesn’t make sense in the real world. It is not possible that the duration
of a dive is near t = 0, because it’s too short for a dive.
Example 2: A study was done to see the relationship between the time it takes, to complete a college degree and the
student loan debt sustained, y. The equation of the regression line is as follows:
y=24152 + 14430 x
Interpret the slope of the regression line in the context of the study.
Solution: First, note that m is the slope which is the coefficient in front of x. Thus, the slope is 14,430. Next, the slope is
taken as rise over run, so:
rise 14430
Slope = =
run 1
The rise is the change in y and y denotes student loan debt. The numerator signifies an increase of amount of 14,430 of
student loan debt. The run is the change in x the time it takes to complete a college degree. Thus, the denominator
represents a rise of 1 year to complete a college degree.
Comments: We can deduce the slope as telling us that for every extra year it takes to finish college, on an average, the
student loan debt heightens by an amount of 14,430.
Example 3: Suppose that the LDL cholesterol levels of a sample of 45-year-old women were tested. Then the doctors
waited several years to see the connection between a woman's cholesterol level in mg/dl, x, and her age of death, y. The
equation of the regression line was found to be:
y=104−0.3x
Interpret the slope of the regression line in the context of the study.
Solution: The slope of the regression line is –0.3. The slope as a fraction is:
rise –0.3
Slope = =
run 1
The rise change in y and y gives the age of death. Since the slope is negative, the numerator indicates a decrease in
life expectancy. Thus, the numerator represents a decrease in lifespan of 0.3 years.
The run denotes change in x and x the cholesterol level. Thus, the denominator shows a cholesterol level increase of
1 mg/dl.
Comments: The slope tells us that for every extra 1 mg/dl of LDL cholesterol, on an average, women are forecast to die
0.3 years earlier.
Regression 281

