1 Lesson Shapes of Scatterplots

2 Lesson Shapes of Scatterplots California Standard: Statistics, Data Analysis, and Probability 1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level). What it means for you: You’ll learn about different types of correlation and what they look like on scatterplots. Key words: slope positive correlation negative correlation strong correlation

3 Shapes of Scatterplots Lesson In the last Lesson, you learned how to make scatterplots from sets of data. By looking at the pattern of the points in a scatterplot, you can decide how the variables are related — for example, whether ice cream sales really do increase on hot days.

4 Shapes of Scatterplots Positive Slope Means Positive Correlation Lesson If two things are correlated, they are related to each other — if one changes, the other will too. Two variables are positively correlated if one variable increases when the other does. For example, children’s heights are positively correlated with their ages — because older children are typically taller than younger ones. Variables are positively correlated if one variable increases as the other does.

5 Shapes of Scatterplots If two positively correlated variables are plotted on a scatterplot, the points will lie in a band from bottom left to top right. If you were to draw a line through the points it would have a positive slope. Lesson The thinner the band of points on the scatterplot, the more strongly correlated the data is. This graph shows positive correlation. This graph shows strong positive correlation.

6 Shapes of Scatterplots Negative Slope Means Negative Correlation Lesson Negative correlation is when one quantity increases as another decreases. For example, values of cars usually decrease as their age increases. Variables are negatively correlated if one variable increases as the other decreases.

7 Shapes of Scatterplots Lesson The thinner the band of points, the more strongly correlated the data is. This graph shows negative correlation. This graph shows strong negative correlation. If a scatterplot shows negative correlation, the points will lie in a band from top left to bottom right. They’ll follow a line with a negative slope.

8 Shapes of Scatterplots No Obvious Correlation Means Random Distribution Lesson When points seem to be spread randomly all over the scatterplot, then it is said that there is no obvious correlation. For example, people’s heights and their test scores are not correlated — the height of a person has no effect on their expected test score. This graph shows no obvious correlation.

9 Shapes of Scatterplots Example 1 Solution follows… Lesson Describe the correlation shown in the scatterplot opposite. Solution The correlation is fairly strong — the points lie in a fairly narrow band. The plot shows positive correlation. (As the temperature increases, the number of ice creams sold tends to increase.) Temperature (°F) Number of ice creams sold

10 Shapes of Scatterplots Lesson If it was perfect the points would lie in a straight line, as shown on the left. The correlation in Example 1 is strong, but it isn’t perfect Temperature (°F) Number of ice creams sold Temperature (°F) Number of ice creams sold

11 Shapes of Scatterplots Guided Practice Solution follows… Lesson In Exercises 1–2, describe the type of correlation % of households with burglar alarms No. of burglaries per 1000 people Amount of gasoline sold on street B per day ($) No. of cars using street A per day negative no correlation

12 Shapes of Scatterplots Guided Practice Solution follows… Lesson In Exercises 3–4, describe the type of correlation Average test score (%) Attendance (%) Grade level Time spent on homework per day (h) positivestrong positive

13 Shapes of Scatterplots Independent Practice Solution follows… Lesson Brandon investigates the relationship between the number of spectators at a football game and the amount of money taken at the concession stand. What kind of correlation would you expect? 2. If every job you do takes one job off your to-do list, what kind of correlation would you expect between the number of jobs you do and the number of jobs on your to-do list? positive negative

14 Shapes of Scatterplots Independent Practice Solution follows… Lesson In Exercises 3–4, describe the correlation shown End of year test score No. of days absent from school perfect positive correlation weak negative correlation Length of square (in) Width of square (in)

15 Shapes of Scatterplots Lesson Round Up If the points lie roughly in a diagonal line across a scatterplot, it means the variables are correlated. An “uphill” band means positive correlation, whereas a “downhill” band means negative correlation. Positive correlation Negative correlation