Introducing Statistics 5: Relationships

19 flashcards · Mathematics · by lakesare

1. Give an example of two "variables" being "related"?

   Knowing girl's height helps you guess the girl's age.

2. What's paired data?

   When we have: 2 variables for a single sampling unit

3. [Scatterplots] Visually imagine response variable VS explanatory variable.

4. [Scatterplots] Visually imagine: positively related variables VS negatively related variables. There is a definite relationship between time of day and number of casualties, but it is much more complex than one that can be described simply as either positive or negative.

   positively related variables negatively related variables

5. [Scatterplots] Visually imagine: linear relationship VS non-linear relationship.

   linear relationship non-linear relationship

6. [Scatterplots] Visually imagine: strong relationship VS weak relationship.

   strong relationship weak relationship Notice that in this scatterplot the overall pattern is not very clear. The points go generally up as you move from left to right. However, there is lots of scatter around whatever trend there is. So there is a weak relationship between the average consumption in metered households and the average consumption in unmetered households served by the same company. Deciding when a relationship is clear enough to be a 'strong' relationship is a subjective judgemen…

7. [Regression] What's regression in statistics?

   The process if finding a line that best represents a relationship. An example of looking at the scatterplot and choosing a line that appears to provide a sensible model for the pattern made by the points.

8. [Regression] Which regression is better? Yield from an industrial process Yield from an industrial process, with a summary line going through all data points

   1st, because the simplest adequate curve should be chosen.

9. [Regression] What do we call this red line? Yield from an industrial process

   Fitted line.

10. [Regression] What are the black think lines from the fitted line to the data?

    These are the residuals. The short, thicker lines from the fitted line to the data points are the residuals.

11. [Regression methods] Name 2 methods of fitting a line to the data. Yield from an industrial process

    fitting by eye least squares y = a + bx

12. [Regression] What does DFR stand for?

    Data = Fit + Residual

13. [Regression] Imagine Data = Fit + Residual on this image.

    Note that a 'Residual' is the vertical distance between a data point and the line. The 'Residual' is positive if the line is below the data point, and the 'Residual' is negative if the line is above the data point. If the 'Residual' is zero, the data point lies exactly on the fitted line.

14. [Regression] What should a perfect residual plot look like?

    It should have no pattern. The residuals are generally evenly balanced, positive and negative, with the positive residuals spread through the range of the explanatory variable. So the line fits the data well.

15. [Regression methods: least squares] How to calculate the least squares regression line?

    Find the slope Find the y-intercept

16. [Regression methods: least squares] In "least squares regression", "least squares" of what?

    Least squares of residuals: the slope minimizes ∑(residual2 + ...residual2). A line is a good fit to a batch of data if the residuals are small.

17. [Regression methods: least squares] Linear regression line VS linear regression?

    linear regression line - the actual red line y = a + bx linear regression - the process of finding the line y = a + bx.

18. [Regression methods: least squares] Why is it so that we can only predict: from the explanatory variable to the response variable?

    Because minimising: squared vertical distances VS squared horizontal distances on a scatterplot leads to different results.

19. [Regression] Why is calculating residuals useful?

    It lets us estimate the fit of a regression line.