Interpretation Unit #8 - Statistics

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 and 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 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 (even if no miles are driven).

Examples Interpret the slope and y-intercept of the model.

Examples Answers 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 (even if no minutes are used). Slope: There has been a $19.25 increase in monthly disability benefits for every year after 1990. Y-Intercept: In 1990, the monthly disability benefit was $585.72.

Correlation vs. Causation Just because two variables have a high correlation (r-value) does not mean that one causes the other. The only way to prove causation is through experimentation (not just a study) Two variables can be related without causing one another.

Example 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?

Example A study of 30 developing nations find a strong correlation (r = .82) between the number of radio stations per capita and the number of new cancer cases reported each year. Do radio stations cause cancer? Are there any other factors or causes to consider?