# 13 Statistics Questions

1. Does correlation equal causality? Why or why not? What is the difference between strong positive and strong negative correlation?

2. How would you determine if this correlation is real in the population? Is there value in a strong negative correlation? If so, what? What does zero correlation tell you?

3. What does r tell you? What does r2 tell you? What does 1- r2 tell you? What does it mean?

Label each of the following situations "P" if it is an example of parametric data or "NP" if it is an example of nonparametric data.

4. In a comparison of two towns, is the average height of its residents the same? _____

5. A manufacturer produces a batch of memory chips (RAM) and measures the mean-time-between-failures (MTBF). The manufacturer then changes a manufacturing process and produces another batch and again measures the MTBF. Did the change to the process improve the MTBF? _____

6. The average life span of a dog is proportional to the amount of calcium consumed. _____

7. The correlation between gene disorders and certain diseases. _____

8. From a written survey where the respondents were asked to rate an individual on a scale of 1 to 5, one group rated an individual a 3.7, another group rated the individual a 4.3. Is the difference statistically significant? _____

9. A study of vehicle accidents on a military installation compared to drivers' rank. _____

10. Show that the numbers drawn in a state lottery are truly random. _____

11. There is a direct correlation to a student's grade and the student's rating of an instructor. _____

12. What assumptions are required in using the multiple regression model?

13. In simple linear regression, the regression equation is a straight line. In multiple regression, what geometric form is taken by the regression equation when there are two independent variables? When there are three or more independent variables?

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Answer

1. Does correlation equal causality? Why or why not? What is the difference between strong positive and strong negative correlation?

Correlation relates to how independent two variables are from one another. If two things are highly correlated, they are not independent at all, and vice versa. A "strong" correlation will be relatively close to -1 or +1, and a weak correlation will be closer to 0. When two variables have a strong positive correlation (close to +1), when one variable increases, the other also increases. When two variables have a strong negative correlation (close to -1), when one variable increases, the other decreases.

Note that variables can be strongly related, but have a coefficient of 0. This can happen if they are not linearly related. Also, a strong correlation does not imply a causal relationship between the variables: maybe the both increase at the same time by coincidence, or a third factor is influencing them both.

A good example of correlative vs causation is that ice cream sales are strongly negatively correlated with snow-shovel sales. Is this because the sale of ice cream prevents the sale of snow shovels in some way (or vice versa)? If that were the case, there would be a causal relationship. Instead, it's the weather that is affecting both: ice cream is sold more in the summer than in the winter and the opposite is true for snow shovels. There is a correlation but not a causation.

2. How would you determine if this correlation is real in the population? Is there value in a strong negative correlation? If so, what? What does zero correlation tell you?

You would take a sample from the population and see what the sample correlation is. If you ...