Scatter Plots A scatter plot is a graph that displays data points for the purpose of determining if a relationship exists between the points. Scatter plots are used to show how closely the data points fit to a line or a curve.

Line of Best Fit A line of best fit can sometimes be drawn on a scatter plot to represent a set of data. From looking at the line of best fit, you can make predictions for data that is not present.

Draw a scatter plot of the data and then draw a reasonable line of best fit.

2) Will studying longer affect test grades? a. Draw a scatter plot of the data b. Draw a line a best fit.   c. Can you estimate what grade a person would get if they studied for 4 hours?

Correlation Looking at a scatter plot is a way to determine if a correlation exists between two variables. A positive correlation is when both variables increase or decrease together. A negative correlation occurs when one variable increases and the other variable decreases. If the data points are randomly scattered, then there is little or no correlation.

Little or No Correlation 3) Positive Correlation Negative Correlation Little or No Correlation

4) If the data points are close to the line of best fit, it is said to have a strong correlation. Weak Positive Strong Positive Weak Negative Strong Negative

Correlation: Relationship Types of Correlations 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 quadratic cubic 𝑦=𝑎 𝑥 3 +𝑏 𝑥 2 +𝑐𝑥+𝑑

5) a) What type of correlation does this scatter plot have? Is this a strong correlation or a weak correlation?

5) b) What type of correlation does this scatter plot have? Is this a strong correlation or a weak correlation?

5) c) What type of correlation does this scatter plot have? Is this a strong correlation or a weak correlation?

6) a. Construct a scatter plot b. What type of correlation? x Y 1 2 4 6 15 8 30 10 60   a. Construct a scatter plot b. What type of correlation? c. Strong or weak correlation? d. Can you draw a line of best fit.

7) Is there a relationship between number of cell phone calls and age, or does it look like the data points are scattered? If there is a relationship between number of cell phone calls and age, does the relationship appear to be linear?

8) Is there a relationship between moisture content and frying time, or do the data points look scattered? If there is a relationship between moisture content and frying time, does the relationship look linear? Then what does the relationship look like? Data Source: Journal of Food Processing and Preservation, 1995

9) This scatter plot shows data for the prices of bike helmets and the quality ratings of the helmets. Is there a relationship between quality rating and price, or are the data points scattered? If there is a relationship between quality rating and price for bike helmets, does the relationship appear to be linear? Data Source: www.consumerreports.org/health

10) Is there a relationship between finish time and age, or are the data points scattered? Do you think there is a relationship between finish time and age? If so, does it look linear? Then what does the relationship look like? Data Source: Sample of 6 women who ran the 2003 NYC marathon

11) A mare is a female horse and a foal is a baby horse. Is there a relationship between a foal’s birth weight and a mare weight, or are the data points scattered? If there is a relationship between baby birth weight and mother’s age, does the relationship look linear? Data Source: Animal Behaviour, 1999

12) The scatter plot below shows the profit, by month, for a new company for the first year of operation. Kate drew a line of best fit, as shown in the diagram. Using this line, what is the best estimate for profit in the 18th month?

13) For 10 days, Romero kept a record of the number of hours he spent listening to music. The information is shown in the table below. Which scatter plot shows Romero’s data graphically? 1) 3) 2) 4)

14). The scatter plot below shows the number of hours of sleep 14) The scatter plot below shows the number of hours of sleep from Tuesday night and the corresponding test score from Wednesday for students in Mr. Dusenbury’s social studies class. Based on a line of best fit, what would be the predicted number of hours of sleep for a student who scored an 85 on the test?

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