Interpretation4.12 - Statistics

Interpreting Slope in ContextSlope tells us the change in the y-variable

per change in x-variable.When interpreting slope in context, always

put it in terms of an increase in 1 unit of x (decimals).

Interpret the slope:There is a $0.25 increase in cost for every 1 mile driven.

Interpreting the y-intercept in ContextThe y-intercept is the value when x

equals what?Normally, this tells us an initial value.

Interpret the y-intercept:There is a flat fee of $35 to rent the truck (if 0 miles are driven).

Examples2. Interpret the slope and y-intercept of

the model.

Slope: There is a $0.38 increase in cost for every 1 minute used.Y-Intercept: There is a $5 monthly fee for this plan (if zero minutes are used).

Correlation vs. Causation Just because two variables have a high correlation

(r-value) does not mean that one causes the other. Correlation simply means two variables are related

The only way to prove causation is through experimentation (not just a study) For example, in medical research, a sample population might be split into two, with one group receiving a placebo and the other the actual medication. Causation can be monitored in this format.

Two variables can be related without causing one another.

Let’s Examine this further…Statistical Language - Correlation and Causation

Example4. A study of 50 cities in North America

finds a strong correlation (r =.75) between the number of teachers employed in a city and the dog food sales in the city. Are the teachers encouraging people to buy dog food? Are there any other factors or causes to consider?

• This is an example of correlation without causation

• Other factors: population could be increasing, therefore more dog food is being purchased