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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.





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