1. Lesson 4.1 Bivariate Data Today, we will learn to …
> construct and use tables showing two different variables obtained from the same population

2. Bivariate Data
The values of two different variables that are obtained from the same population.
1) both qualitative (attributes)
2) one qualitative - one quantitative
3) both quantitative (numerical)

3. TWO QUALITATIVE VARIABLES
Examples?
gender & favorite sport
gender & favorite class
cell phone & grade level

4. Senior Survey Activity
Male
Females
Total
Has a Car 95 78
173
No Car 81 68
149
176
146
322
What percentage of the teens have cars?
How many students were surveyed?
173
322
322
54%
What type of variables are used?
What percentage of the boys had cars? 95
176
two qualitative variables
54%

5. ONE QUALITATIVE &
ONE QUANTITATIVE
Examples?
Gender & Height
Vehicle & Cost
Vehicle & MPG

6. Guys & Height
Girls & Height

7. TWO QUANTITATIVE VARIABLES
Examples?
age & height
years employed & salary
height & weight

8. The number of hours studied, x, compared to the grade earned, y
90 –
80 –
70 –
60 –
number of hours spent studying
Exam Grade
The number of hours studied, x, compared to the grade earned, y

9. y x
negative linear correlation

10. y x
positive linear correlation

11. y x
no linear correlation

12. y x
no correlation

13. A marketing manager conducted a study to find out if there is a
A marketing manager conducted a study to find out if there is a relation between
money spent on advertising
and sales.
What do you predict?

14. Enter the data into List 1 and List 2
Advertising
in 1000s
Sales
2.4
225
1.6
184
2.0
220
2.6
240
1.4
180
186
2.2
215
Enter the data into List 1 and List 2

15. 2nd Press Press Turn On Plot 1 Type: Scatter Plot
ENTER
Press
Turn On Plot 1
Type: Scatter Plot
Identify lists: L1 and L2
WINDOW
Press
and set dimensions
Go to next slide

16. Advertising
in 1000s
Sales
2.4
225
1.6
184
2.0
220
2.6
240
1.4
180
186
2.2
215
There is a positive correlation between $$ spent on advertising and sales
Xmin = _____
Xmax = _____
Xscl = _____
Ymin = _____
Ymax = _____
Yscl = _____ 3 1
150
250 25

17. correlation coefficient
The correlation coefficient
is a number r that represents
the relationship between the two variables
correlation coefficient
–1 < r < 1

18. If r is close to –1, there is a strong negative correlation.
This means as
x increases, y decreases
If r is close to 1, there is a
strong positive correlation.
This means as
x increases, y also increases
If r is close to 0, there is
no linear correlation.

19. 5 types of correlations
Strong Positive
Strong Negative
Negative
Positive
Weak Negative
Weak Positive
No Correlation
as “x” increases,
“y” decreases
as “x” increases,
“y” increases
What do they mean?

20. -1 -.9 -.8 -.7 -.6 -.5 -.4 -.3 -.2 -.1 0 .1 no correlation
Strong Negative Weak
Negative Negative
no correlation
Weak Positive Strong
Positive Positive

21. Identify the type of correlation
a) r = 0.81
Strong positive
b) r = – 0.92
Strong negative
c) r = 0.45
Weak positive
d) r = 0.05
none
e) r = – 0.35
Weak negative

22. Enter the two lists into two stat lists.
Advertising
in 1000s
Sales
2.4
225
1.6
184
2.0
220
2.6
240
1.4
180
186
2.2
215
2nd
Press
Cursor to Diagnostic On
ENTER
Press
twice

23. Press Cursor to CALC Choose 4: LinReg (ax+b) Identify lists L1 , L2
STAT
Cursor to CALC
Choose 4: LinReg (ax+b)
Identify lists L1 , L2
ENTER
Press

24. As x increases, y ___________
Correlation coefficient?
r =
0.913
Type of correlation?
Strong positive correlation
increases
As x increases, y ___________
Conclusion:
As $$ spent on ads increases,
sales ____________
increase

25. It's Time To
Practice!

26. Lesson 4.2 Linear Regression Today, we will learn to…
> write an equation that explains
a linear correlation

27. n is the number of pairs of data
We need to determine if our sample can be used to represent the entire population.
Use the Critical Values Table
n is the number of pairs of data

28. level of significance (α )
Using α = means that
we might be wrong ___% of the time 5
Using α = means that we might be wrong __ % of the time. 1
Which is better?
A 0.01 level of significance
is better!!

29. Our study is significant. The sample represents the population
n = 5 pairs of data r =
level of significance level of significance
α = α = 0.01
critical value = critical value = 0.959
| r | = _______
0.893
0.893 > 0.878?
0.893 > 0.959?
YES NO
Our study is significant. The sample represents the population
with a 5% error

30. n = 10 r = 0.950
| r | =
0.950
level of significance level of significance
α = α = 0.01
critical value = critical value = 0.765
0.950 > 0.632?
0.950 > 0.765?
YES
YES
Our study is significant. The sample represents the population
with a 1% error

31. level of significance level of significance
n = 7 r =
| r | =
0.750
level of significance level of significance
α = α = 0.01
critical value = critical value = 0.875
0.750 > 0.754?
0.750 > 0.875? NO NO
Our study is not significant. The sample does not represents the population.

32. | r | > C.V. ? | r | > C.V. ? yes yes yes no no no
α = α = 0.01
| r | > C.V. ?
| r | > C.V. ?
yes
yes
The study is significant. The sample represents the population with a 1% error
yes no
The study is significant. The sample represents the population with a 5% error no no
The study is NOT significant. The sample does not represent the population.

33. The fact that two variables are strongly correlated does
not always prove a
cause-and-effect relationship between the variables.
1) Does x cause y?
2) Should the variables be reversed? Does y cause x?
3) Could the relationship be caused by a third variable?
4) Could the relationship be a coincidence?

34. In many communities, there is a strong positive correlation between the amount of ice cream sold in a given month
and the number of drownings that occur in that month. Does this mean that ice cream causes drowning? If not, what is an alternative explanation for the strong correlation?

35. It's Time To
Practice!

36. Lesson 4.3 Linear Regression Today, we will learn to…
> write an equation that explains
a linear correlation

37. A linear regression line is a line of best fit for a scatter plot.
The equation of a regression line is y = m x + b
slope
y-intercept

38. LinReg(ax+b) L1 , L2 a = – 4.3 b = 96.8 y = – 4x + 97 domain: Grade
Absences
Grade 1 95 7 65 3 80 2 85 5 77 4 70 93 75 82
LinReg(ax+b) L1 , L2
a = – 4.3
b = 96.8
y = – 4x + 97
domain:
1 < x < 7

39. You can use the equation to make predictions if the correlation between x and y is significant.
For our example with absences
and grades, the regression line is
y = – 4x + 97
Predict the expected grade of someone with 1 absence.
93%
- 4(1) + 97

40. It is not meaningful to predict the value of y for x = 25 because
For our example with absences and grades, y = – 4x + 97
Predict the expected grade of someone with 25 absence.
It is not meaningful to predict the value of y for x = 25 because
25 is outside the domain.
Does this make sense?
- 4(25) + 97
- 3%

41. The x-values must fall within the domain of the sample in order to use the equation to make predictions.
IMPORTANT!

42. It's Time To
Practice!