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# Interpreting the Slope of the Linear Regression Line

Interpreting the Slope of the Linear Regression Line

Provide an interpretation in a single sentence that includes the following information:

1. It tells you what the variables are
2. It lets you know whether the dependent variable increases or decreases as the independent variable increases
3. 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.

Here is one example:
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.

Notice that all these interpretations follow a pattern:

i) For every "I unit" increase in "x", "y" "increases or
decreases" by "slope" "units."
ii) 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.

Now, you try for the following problems and add as many problem as you can to the list please and carry a discussion on the X, Y, and the slope value, when needed;

1. For the problem involving price and number of stereos sold.

2. For the problem involving length and weights of alligators.

3. For the problem involving additional story that a building contains.

4. For problem involving additional ounce of laundry detergent in a package of laundry detergent and the price increases.

The following is for your information that helps the answer for this question.

In a linear relation we are facing 2 variables, X & Y. X is independent and Y is your dependent variable. Your linear relationship has a slope. It is positive, when X increases will cause Y value to increase too. The slope will be negative, when increase in X values will cause the Y values to decrease.

So, you will design a linear relation for each of the given situation and think about the slope being -ve, or +ve. Then, describe the problem in one sentence as shown in the example.

#### Solution Preview

1. For the problem involving price and number of stereos sold.

For every \$30 increase in the price, the number of stereos sold decreases by 3

2. For the problem involving length and weights of alligators.

For every 1 inch ...

#### Solution Summary

This solution addresses what the slope of the regression line would mean in each of the four scenarios and describes one original scenario. This solution is 181 words.

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