Review for Test Chapters 1 & 2: Go over HW’s, quizzes, & DG’s p. 106 #60, 61, 63, 66, 67, 68, 70 p. 162 #51, 53, 54, 55, 57 - 60

Advanced Placement Statistics Section 3 Advanced Placement Statistics Section 3.1: Scatterplots and Correlation EQ: How do you describe an association between variables on a scatterplot?

RECALL: Up to this point we have only discussed Univariate Data --- data from only 1 variable of interest Ex. a) age of students in the class b) number of cars in the parking lot c) hair color

New Terms to Know: Could be: 1. both qualitative 2. both quantitative Bivariate Data --- values of 2 different variables from the same population of interest. 1. both qualitative Could be: 2. both quantitative 3. one of each

Response Variable --- the outcome variable (Dependent Variable) Explanatory Variable --- the variable that explains ( or predicts changes) in the response variable; (Independent Variable) Response DEPENDS ON Explanatory In Class Assignment: p. 173 – 174 #1 – 4

3. 1 a) Time is the explanatory variable 3.1 a) Time is the explanatory variable. Grade on the exam is the response variable. 3.1 b) Height is the explanatory variable. Weight is the response variable. 3.1 c) Inches of rainfall is the explanatory variable. Yield of corn is the response variable. 3.1 d) No defined explanatory and response variable. You would need to explore the relationship between these variables 3.1 e) Family income is the explanatory variable. Years of education completed by the child is the response variable.

3. 2 Weight of a person is the explanatory variable 3.2 Weight of a person is the explanatory variable. Mortality rate over a 10 year period is the response variable. Other variable that could impact the relationship might be physical activity and/or economic status. 3.3 Water temperature is the explanatory variable. Weight change is the response variable. Both are quantitative variables. 3.4 Type of treatment is categorical and is the explanatory variable. Survival time is quantitative and the response variable.

Scatterplot--- graphical display of two quantitative variables Explanatory Variables Independent Variables Response Variables Dependent Variables

Alcohol-related deaths and consumption Does alcohol consumption explain the number of deaths from cirrhosis?

Association --- exists if a particular value for one variable is more likely to occur with certain values of the other variable; Must discuss in terms of direction, strength, and linearity.

Describe the association shown in each scatterplot below: Very strong, positive, linear Moderately strong, positive, linear Weak, negative, linear No association

Scatterplots Illustrating Bivariate Relationships

Creating A Scatterplot On Your Graphing Calculator: Technology Toolbox p. 183 [BEER] [BAC] Data found on p. 177. Assignment: p. 179 – 184 #5 - 10

EQ: What is correlation coefficient and what does it tell you about the association between two variables? Correlation Coefficient measures association -1 < r < 1

A correlation greater than 0.8 would be described as strong. A perfect correlation of ± 1 occurs only when the data points all lie exactly on a straight line. A correlation greater than 0.8 would be described as strong. A correlation less than 0.5 would be described as weak. NOTE: Correlation between 0.5 and 0.8 can be described as moderate.

Correlation makes no distinction between explanatory and response variables. It makes no difference which variable you call x and which you call y when calculating the correlation. r does not have units. Changing the units on your data will NOT affect the value of the correlation.

Correlation describes only LINEAR relationships between two variables. Correlation does not imply cause and effect, even at very strong values for r. r is very strongly affected by OUTLIERS. Use r with caution when outliers appear in your scatter plot. Don’t rely on r alone to determine the linear strength between two variables. Graph a SCATTERPLOT first.

The correlation coefficient takes the subjectivity out of interpreting scatterplots. You might think two variables have a strong correlation because of how the scatterplot looks, but the value of r might reveal something different (see image below). The two scatterplots to the left represent the same set of data…but does one look stronger than the other?

CORRELATION DOES NOT IMPLY CAUSATION!!! Guideline for Interpreting Correlation Coefficient:

Calculating Correlation Coefficient: Technology Toolbox p. 210 only [NEA] [FAT] Use the Data on p. 200   Assignment: pp. 193 – 195 #15, 16, 18, 19 pp 196 – 199 #21,23,24,25, 28