Scatterplots And Correlation PDF

September 20, 2023 Chapter 3 Describing Relationships 3.1 Scatterplots and Correlation  September 20, 2023 Explanatory and Response Variables Explanatory Variable: explains or influences changes in respons...

September 20, 2023 Chapter 3 Describing Relationships 3.1 Scatterplots and Correlation  September 20, 2023 Explanatory and Response Variables Explanatory Variable: explains or influences changes in response variable (amount of rain) AKA independent variable Response Variable: measurement for outcome of a study (weed growth) AKA dependent variable Note: In many studies, the goal is to show that changes in one or more explanatory variables actually cause changes in a response variable. However, other explanatory-response relationships don’t involve direct causation.  September 20, 2023 Scatterplots Shows the relationship between two quantitative variables measured on the same individuals. Explanatory variable on x-axis, Response variable on y-axis. *label and scale axes *each individual is a data point  September 20, 2023 Scatterplots Each member of a small class ran a 40 yard sprint and then did a long jump with a running start. The table shows sprint time (sec) and jump distance (inches). Make a scatterplot of the relationship between these two variables. Sprint Time (s) Jump Length (in) 5.41 171 5.05 184 7.01 90 7.17 65 6.73 78 5.68 130 5.78 173 6.31 143 6.44 92 6.50 139 6.80 120 7.25 110  September 20, 2023 Interpreting Scatterplots D irection (positive, negative, no) U nusual features (outliers or clusters) F orm (linear/nonlinear) S trength (weak/moderate/strong) Describe association using the above in context (name both variables) September 20, 2023  September 20, 2023 Manatees are often injured or killed by boats. The table shows the number of boats registered in Florida (in thousands) and the number of manatees killed by boats in 1977-2007. Use a calculator to make a scatterplot and describe any association you see.  September 20, 2023 The scatterplot shows interval (in minutes) between eruptions of Old Faithful against the duration of the eruption. 1. Describe the direction of the relationship. Why does this make sense? 2. What form does the relationship take? Why are there two clusters? 3. How strong is the relationship? 4. Are there any outliers? 5. What information do you need to predict when the next eruption will occur?  September 20, 2023 IMPORTANT Association (correlation) does NOT IMPLY CAUSATION Think about other factors that may influence/create the relationship you see.  September 20, 2023 Measuring Linear Association  September 20, 2023 Now, let's play "Guess the Correlation"!  September 20, 2023 Make a scatterplot with r close to 0.7 Use 10 points. You can drag points to move them after they are placed. Now stack 9 points, and 1 to the far right. Move this point until the correlation is close to 0.7 Can you make a curved plot with r about 0.7?  September 20, 2023 Facts about Correlation  September 20, 2023 Facts about Correlation ~ Correlation only applies to pairs of quantitative variables ~ Correlation makes no distinction between explanatory and response variables ~r is not affected by units ~r is unitless ~Correlation measures strength of linear relationships ~ r is STRONGLY affected by outliers ~Correlation is not a summary  September 20, 2023 Facts about Correlation Does play video games help you get a degree? Computer science majors are often gamers, frequenting the local arcades. Are the arcade games helping them earn a doctorate in computer science? This is a scatterplot created using US data for 2000-2009. The explanatory variable is arcade revenue, and response is number of doctoral degrees awarded. a) Will playing lots of video games at the arcade make you more likely to get a computer science doctorate? Explain. b) What effect does the year 2008 ($1803 million in revenue, 1787 doctorates) have on the correlation? Explain.  September 20, 2023 36.1 54.6 48.5 42.0 50.6 42.0 40.3 33.1 42.4 34.5 51.1 41.2 Mass Rate 995 1425 1396 1418 1502 1256 1189 913 1124 1052 1347 1204