Interpreting the Slope of the Linear Regression Line
in the context of the problem by Roberta Bloom.
You are to provide an interpretation in a single sentence that includes the following information:
It tells you what the variables are
It lets you know whether the dependent variable increases or decreases as the
independent variable increases
It tells you how much this increase is.
The sentence should be understandable to people who are not taking statistics and don't even
know any algebra. Part of your job as a statistician is to make sense of the statistics in a way
that “ordinary people” can understand.
Pretend you are a reporter writing the sentence in the newspaper for everyone to read or you
are writing the script for the TV news announcer. You are NOT writing to your math teacher or
a statistician.
The slope can be interpreted in a single sentence. If stated correctly this sentence can be much
easier to understand than a whole paragraph.
(Yes, I will be particular about this interpretation when I am grading your projects.)
Here are some examples.
For the problem relating cigarette sales and lung cancer deaths:
For every additional 100 cigarettes sold per capita, the lung cancer death rate increases by .352
deaths per 100,000 people.
For the problem involving price and number of steroes sold that we did in class:
For every $1 increase in price, the number of stereos sold decreases by .68
For the problem involving length and wieghts of alligators that I talked about in class:
For every one inch increase in length, the weight of an alligator increases by 2.43 pounds.
For problem 5 in chapter 12 on the homework:
For each additional story that a building contains, the height of the building increases by
11.7587 feet.
For problem 9 in chapter 12 on the homework:
For each additional ounce of laundry detergent in a package of laundry detergent, the price
increases by $.0317, or 3.17 cents.
Notice that all these interpretations follow a pattern:
For every “I unit” increase in “x”, “y” “increases or decreases” by “slope” “units”
Everything in quotes should be described as appropriate for the particular problem, including
appropriate descriptions of x and y, the units of each, whether the change is an increase or
decrease, and the amount of change where “slope” is indicated. The letters x and y should not
appear in your interpretation.