RELATIONSHIPS Vocabulary scatter plot correlation A scatter plot is a graph with points plotted to show a possible relationship between ordered pairs. A scatter plot is an effective way to display types of data. Displaying data visually can help you see relationships. correlation describes a relationship between two data sets. A graph may show the correlation between data. The correlation can help you analyze trends and make predictions. There are three types of correlations between data. Vocabulary scatter plot correlation positive correlation negative correlation no correlation trend line

3 TYPES OF RELATIONSHIP RELATIONSHIP (relationship between the x values & the y values.) Up to Right Up to Left “PQR” “LMN” 1 4 -1 4 -1 -4 _ 1 4 1 -4

What do you think the relationship between ice cream sales and weather temperature are? 3

As one set of values increase, the other set increases. POSITIVE As one set of values increase, the other set increases. 4

Describe the correlation illustrated by the scatter plot. As the years passed, the number of participants in the snowboarding competition increased. There is a positive correlation between the two data sets.

OUTLIERS

Outliers Outlier a number far above or below the data set considered abnormal and of questionable accuracy.

Find the outliers outliers

Unusual points in a scatter plot

LINE OF BEST FIT OR TREND LINES from Scatter Plots

Is there a relationship between your height and shoe size? 45 42 39 36 33 30 27 Can you predict how big a foot someone would be with a height of 96 inches? Foot length (cm) 24 21 18 15 12 9 6 3 8 16 24 32 40 48 56 64 72 80 88 96 104 height (inches) 13

Approximating a Best-Fitting Line Years since 1900 Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 SOLUTION (96, 230). (96, 230) Find two points that lie on the best-fitting line, such as (8, 138) and (96, 230). (8, 138) Find the slope of the line through these points.

Write an equation of your line. Approximating a Best-Fitting Line Years since 1900 Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 DISCUS THROWS The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws. Write an equation of your line.

LINEAR VS NON LINEAR from Scatter Plots

(equation whose graph forms a line.) Linear Equation: (equation whose graph forms a line.) y = x + 1 18

IS this a Linear equation? y = –2x + 3 8 y 6 8 4 2 x x 4 4 8 –2 2 4 –4 Non linear linear 19

A C E B D F

IS this a Linear equation? –3x + 2 = y y = |x + 3|   linear Non linear 21

STRONG AND WEAK ASSOCIATIONS from Scatter Plots

Strength and RELATIONSHIPS from Scatter Plots

What type of relationship, positive, negative, or none, is shown by each scatter plot?

Neither the temperature nor the time can be negative. Choose the scatter plot that best represents the relationship between the number of minutes since: an oven was turned off & the temp. of the oven. Explain. Graph B Graph C Graph A This graph shows the temperature of the oven increasing after the oven has been turned off. negative correlation between the time & temp. because oven will get cooler as it is turned off. Neither the temperature nor the time can be negative. Graph B shows negative time, so it is incorrect. Graph C shows the temperature of the oven increasing, so it is incorrect. Graph A is the correct answer.

Fund-Raising Application The scatter plot shows a relationship between the total amount of money collected at the concession stand and the total number of tickets sold at a movie theater. Based on this relationship, predict how much money will be collected at the concession stand when 150 tickets have been sold.

Draw a trend line and use it to make a prediction. Draw a line with about same # points above and below it. It may or may not go through data points. Find point on line whose x-value is 150. y-value is 750. $750 is a reasonable prediction of amount $ collected when 150 tickets sold.

Using the line of best fit shown on the scatter plot, which of the following best approximates the amount of monthly rainfall in month 9? A. B. C. D. 10 inches 11 inches 12 inches 13 inches

The scatter plot shows the relationship between the size of a diamond in Carats and its retail price. Based on these data, what is the approximate retail price of a 0.30 Carat diamond? A. B. C. D. $400 $600 $800 $1000

The graph shows the relationship between a person’s height and weight The graph shows the relationship between a person’s height and weight. Which of the following statements would be an invalid conclusion for these data? A. The graph shows data for 20 people. B. A person who is tall is likely to have a higher weight. C. The tallest person in this study weighed the most. D. A person who has a lower weight has a fast metabolism.