Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The ordered pairs are not connected The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction. We call the relationship between two variables the correlation

Positive Correlation If the x-coordinates and the y- coordinates both increase, then it is POSITIVE CORRELATION. This means that both are going up.

Negative Correlation If the x-coordinates and the y- coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION. This means that 1 is going up and 1 is going down. This means the two are related as opposites.

No Correlation If there seems to be no pattern, and the points looked scattered, then it is no correlation. This means the two are not related.

Scatterplots Which scatterplots below show a linear trend? a) c)e) b) d)f) Negative Correlation Positive Correlation Constant Correlation

Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. Student Time Spent Watching TV Time Spent on Homework Sam Jon Lara Darren Megan Pia Crystal 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 135 min. 120 min. 105 min.

Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TVHomework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 135 min. 120 min. 105 min. Time Watching TV Time on Homework

Describe the relationship between time spent on homework and time spent watching TV. Time Watching TV Time on Homework Trend is decreasing. Trend appears linear. Negative correlation.

Using your GDC to make a scatter plot Enter your data into L1 and L2 GO to STATPLOT, Choose 1: STATPLOT 1 Turn in it on and choose the scatterplot (make sure L1 and L2 are your X and Y) Next go to Zoom and choose 9: ZoomSTAT

Linear Correlation (r) Pearson’s correlation coefficient (r) gives a measure of the linear association between x and y. If x and y are perfectly positively correlated, r = 1 If there is absolutely no association, r = 0 If x and y are perfectly negatively correlated, r = -1 Thus -1 < r < +1 The closer r is to +1 or -1, the greater is the strength of the association.

Possible values for r

Strength of a Correlation

Using only your GDC

Do the “Got It?” problem on your note sheet

Correlation vs. Causation Something to think about There is a 0.91 correlation between ice cream consumption and drowning deaths. Does eating ice cream cause drowning? Does grief cause us to eat more ice cream? Statistics does NOT measure cause

Limitations “Invisible” 3 rd factor (ice cream & drowning) Outliers

Regression Lines Can be added to a scatter plot to help describe trends A regression line is a straight line that describes how a variable y changes as a variable x changes. We often use the regression line for predicting the value of y for a given value of x.

Using the Mean Point

Example Experience (weeks) Typing Speed (wpm)

Example Con’t

Predictions The regression line allows us to make predictions about values for which we have no data You can either use the line on the graph or the equation you found

STEPS FOR THE CALCULATOR Make sure your diagnostics are on Put your x variable values into List 1 and your y variable values into list 2 (STAT, EDIT) STAT CALC Choose #4 LinReg a + bx Enter the locations of your lists Enter

Here is data about the daily temperature and the number of bottles of water sold at the railway station. a)Find the regression equation. b)Describe the correlation Temperature (°C)# bottles sold

Example

Skill Practice Exercise 2.6 #3-9, 13, 15, 19, 27