1. Day 8 Agenda:
Quiz 1.1 & minutes
Begin Ch 3.1
THQ#1 due Tues at beginning of class

3. 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?

4. 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

5. 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

6. 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

7. 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.

8. 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.

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

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

11. 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.

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

13. Scatterplots Illustrating Bivariate Relationships

14. Creating A Scatterplot On Your Graphing Calculator: Technology Toolbox p. 183 [BEER] [BAC]
Data found on p. 177.
Assignment: p – 184 #5 - 10
Review for Test Chapters 1 & 2:
Go over HW’s, quizzes, & DG’s
p #60, 61, 63, 66, 67, 68, 70
p #51, 53, 54, 55,

15. Finish Media Center Day #3
Day 10 Agenda:
DG minutes
Finish Media Center Day #3
Print the calendar and MARK off days as we do the lessons
Review for Test Chapters 1 & 2:
Go over HW’s, quizzes, & DG’s
p #60, 61, 63, 66, 67, 68, 70
p #51, 53, 54, 55,

17. Intent of Question: The goals of this question are 1) to determine your ability to interpret different representations of the same data distribution and 2) to evaluate your ability to determine Normality.
Solution:
a) Since the stem plot shows raw data, you can calculate the mean quiz score for the class. The ogive only shows the cumulative relative frequency of the quiz scores, so you can only obtain information about percentiles and quartiles.
Scoring:
Part a) is essentially correct if the response recognizes that 1) the stem plot shows raw data and the ogive does not and 2) states an appropriate measure such as mean, standard deviation, or range.
Part a) is partially correct if only 1) or 2) is given without comparing plots.
Part a) is incorrect if the response is median, quartiles, or percentiles.

18. Solution:
Using the stemplot, the median would be a score 25. or
Using the ogive, the median quiz score would occur at the 50th percentile
which is approximately 25.
Scoring:
Part b) is essentially correct if the response gives 1) the correct value from the stemplot or 2) states the correct value from the ogive defining it as the 50th percentile.
Part b) is partially correct if the median is defined as the 50th percentile on the ogive, but the wrong value is given.
Part b) is incorrect if the response is different from 25 and no reference is made about finding the 50th percentile on the ogive.

19. Solution:
Graphically: The shape of the stemplot is somewhat skew right and the Normal Probability Plot does not form a straight line. Therefore we can determine this data are not Normally distributed
Numerically: Using the mean = and standard deviation = 13.9 ,
and
Sixteen out of twenty-three students scored in this interval, which is approximately 70% of the class.
and .
All of the students, 100%, scored in this interval. A Normal approximation is not appropriate since this data does not follow the Empirical Rule of
68% - 95% - 99.% for 1, 2, and 3 standard deviations from the mean.

20. Scoring:
Part c) is essentially correct if 1) reference is made to both the stemplot and the NPP and 2) correct calculations are made for standard deviations from the mean and compared to Empirical Rule.
Part c) is partially correct if 1) reference is made to only 1 graph and 2) is complete
or 1) reference is made to both graphs and 2) no calculations are made to compare to Empirical Rule
or 1) no reference is made to either graph and 2) correct calculations are made and compared to Empirical Rule
Part c) is incorrect if no reference is made to either the stemplot or the NPP.

21. SCORE ON QUESTION:

22. EQ: What is correlation coefficient and what does it tell you about the association between two variables?
measurement applicable
to linear association
Correlation
Coefficient
-1 < r < 1
ModeratelyStrong,
positive
Very Strong,
negative

23. 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.

24. 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.

25. 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.

26. 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?
Look at the scale on each x-axis.

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

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