Scatterplots Grade 8: 4.01 & 4.02 Collect, organize, analyze and display data (including scatter plots) to solve problems. Approximate a line of best fit and use to predict.

Scatterplots Scatterplots are used to illustrate data to determine correlations (relationships) between events. Scatter plots will often show at a glance whether a relationship exists between two sets of data.

Gathering Data Let's decide if studying longer will affect math test grades. Given the data on the next slide, a scatter plot has been prepared to represent the data. Remember when making a scatter plot, do NOT connect the dots.

Graphing Data Study hours Test scores TESTSCORETESTSCORE Hours of Study

Analyzing Data The data displayed on the graph resembles a line rising from left to right. Since the slope of the line is positive, there is a positive correlation between the two sets of data. This means that according to this set of data, the longer I study, the better grade I will get on my math test.

Negative Correlation As one variable increases, the other variable decreases. As miles traveled increase, the amount of gas decreased x y

No Correlation Think about the relationship between hair color and intelligence. What do you think the scatterplot would look like? If the plot on the graph is scattered in such a way that it does not approximate a line (it does not appear to rise or fall), there is no correlation between the sets of data. No correlation means that hair color doesn't show any affect on intelligence.

Scatter Plots - $100 ANSWER x y The graph to the right shows what type of correlation?

Scatter Plots - $100 DONE POSITIVE CORRELATION

Scatter Plots - $200 Which of the points could be used to find the equation of the line of best fit? ANSWER x y A) (0, 2) B) (1, –1 ) C) (–1, 2 ) D) (1, –2 )

Scatter Plots - $200 DONE

Scatter Plots - $300 ANSWER In your own words, explain the steps used to find the equation of a line from a scatter plot.

Scatter Plots - $300 DONE Plot the points Draw a line of best fit Find two points ON THE LINE Find the slope between the points Write the equation in point – slope form

Scatter Plots - $400 ANSWER x y Which of the equations could be the equation of the line of best fit? A) B) C) D)

Scatter Plots - $400 DONE

Scatter Plots - $500 ANSWER x y Which of the following statements could be made to reflect the scatter plot if x represents price and y represents purchases? A) As the price increases, the number of purchases increases. B) As the price decreases, the number of purchases increases. C) As the price decreases, the number of purchases decreases. D) There is no correlation between price and purchases.

Scatter Plots - $500 DONE

Line of Best Fit When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight line for purposes of predicting values that may not be displayed on the plot. Such a straight line is called the "line of best fit." It may also be called a "trend" line.

Correlations Determine whether a scatter plot for the following situations would have a positive, negative, or no correlation. 1.Amount of time spent studying and students’ test averages 2.Outside temperature and heating costs 3.Your savings account number and the balance in the account