Scatterplots and Correlations

Transcription

1 Scatterplots and Correlations Section 4.1 1

2 New Definitions Explanatory Variable: (independent, x variable): attempts to explain observed outcome. Response Variable: (dependent, y variable): measures outcome of a study. Example: Grades and number of hours you watch TV 2

3 Scatterplots Purpose: *Display the relationship between two quantitative variables measured on the same individuals.* Explanatory variable should go on x axis. 3

4 Interpreting a Scatterplot 1. Look at overall pattern showing form, direction, and strength of the relationship 2. Look for outliers or other deviations from this pattern. Form: linear relationships, curved relationships, clusters Direction: + Positive Association: the above average values of one variable accompany the above average values of the other variable and below average values tend to occur together. + Negative Association: the above average values of one variable go with below average values of the other variable and vice versa. Strength: determined by how closely the points in the scatterplot follow a clear form 4

5 Examples of Association Give 2 examples of data that display: Positive Association Negative Association No Association 5

6 Positive or Negative 6

7 Positive or Negative 7

8 Positive or Negative 8

9 Positive or Negative 9

10 Changing the Plotting Scales Our eyes are not good judges of how strong a linear relationship is. These 2 scatterplots depict exactly the same data, but the lower/right plot is drawn smaller in a larger field so it appears to show a stronger linear relationship. Correlation is the measure we use to accurately determine how strong or weak a relationship actually is. 10

11 Correlation r (represents correlation) measures the direction and strength of the linear relationship between two quantitative variables Positive r positive association Negative r negative association + r close to 1 or 1: strong linear relationship + r = 1 or 1: perfect linear relationship + r close to 0: very weak linear relationship + r = 0: no linear relationship r, like mean and standard deviation is not resistant to outliers!!!!!!! 11

12 Correlation Value Interpretation 12

13 13

14 Degree days One degree is accumulated for each degree a months average temperature falls below 65oF. Ex. Average temp one month is 20oF. This means there are 45 degree days in this month. This is because = 45 14

15 Using the calculator to find r and determine correlation 15

16 DO NOW Graph a scatter plot and find r for the following data on ice cream sales. 16

17 NOTES "r" does not change when we change units of measurement of either set of numbers. "r" has no unit of measurement; it is just a number. "r" makes no distinction between explanatory and response variables. "r" measures the strength of only a linear relationship between two variables. 17

18 r² r² is the percentage of the variation in y that Is explained by the variation in x Thinking back to the last example, this means that 99% of the gas consumed by the Sanchez household can be explained by the degree days. The other 1% is explained by other reasons such as someone turning the heat up for grandma. We will discuss this more later. 18