1. Interpretation 4.12 - Statistics

2. Interpreting Slope in Context Slope 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.

3. Interpreting the y-intercept in Context The 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).

4. Examples 2. 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).

5. 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.

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

7. Example 4. 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