Introductory Business Statistics International Business School Hanze University of Applied Sciences

1. Hanze University of
Applied Science
Groningen
Ning Ding, PhD
Lecturer of International Business
School (IBS)
n.ding@pl.hanze.nl

2. What we are going to learn?
• Review
• Chapter 12: Simple Regression and Correlation
– dependent / independent variables
– scatter diagrams
– regression analysis
– Least-squares estimating equation
– the coefficient of determination
– the coefficient of correlation

3. Review
• Review What is the interquartile range?
a. 98 b. 1764 c. 854 d.484 e.1940 f.2038
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares Interquartile Range
estimating equation 3-Q1
=Q
–the coefficient of =2205-1721
determination =484
–the coefficient of
correlation

4. Review
• Review
• Chapter 12: L=(8+1)*25%=2.25
Simple Regression
and Correlation Range
Interquartile Q1=133.5
–dependent /
=274.5-133.5
independent
=141 L=(8+1)*75%=6.75
variables
–scatter diagrams
–regression analysis
Q3=274.5
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

5. Median Quartile Decile Percentile
1
1 1st D
2
2 Q1=2
2
2
4
4 Interquartile
5 5 Range
7
7
8
8 Q3=8.5
9
9
12
12 9th D
Boxplot
How to interpret?
http://cnx.org/content/m11192/latest/

6. Review
a. Positive b. Negative
c. Symmetrical d. No idea
a b
Mean= € 450
€ 20 € 2000
Q1= € 250 Median= € 350 Q3= € 850
The distribution is skewed to __________ because the mean is
the right
larger than
__________the median.
http://cnx.org/content/m11192/latest/

7. 0.8
1.0
Mean > Median
1.0
1.2
1.2
1.3
1.5
1.7
2.0
2.0
2.1
2.2
2.0
4.0 Mean < Median
3.2
Positively skewed 3.6
3.7
4.0
4.2
4.2
4.5
4.5
4.6
4.8
http://qudata.com/online/statcalc/ 5.0
Negatively skewed
5.0

8. • Review
This means that the data is
• Chapter 12:
symmetrically distributed.
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Zero skewness
mode=median=mean

9. Regression Analysis
• Review
• Chapter 12:
– scatter diagrams
Simple Regression
and Correlation
– dependent / independent variables
–dependent /
independent – regression analysis
variables
–scatter diagrams – Least-squares estimating equation
–regression analysis
–Least-squares – the coefficient of determination
estimating equation
–the coefficient of – the coefficient of correlation
determination
–the coefficient of
correlation

10. Scatter Diagram
• Review –How to determine both the nature and the
• Chapter 12:
strength of a relationship between variables.
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

11. Describing Relationshi
Scatter Diagram
• Review
Variables – Scatter Diag
Scatter Diagram:
• Chapter 12:
Streudiagramm
Simple Regression Puntenwolk
and Correlation
散布图
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Positive correlation

12. Scatter Diagram
• Review
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Negative correlation

13. catter DiagramDiagram
Scatter Examples
• Review
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
No correlation

14. Scatter Diagram
• Review
Scatter Diagrams:
• Chapter 12: • Patterns indicating that the variables are related
Simple Regression
and Correlation • If related, we can describe the relationship
–dependent /
independent
variables
–scatter diagrams
–regression analysisStrong & Positive Weak & Positive
–Least-squares correlation correlation
estimating equation
–the coefficient of
determination
–the coefficient of No
correlation correlation
Weak & Negative Strong & Negative
correlation correlation

15. Dependent/Independent Variables
Describing Relations
Variables:
Variables – known
• Review
– Independent variables: Scatter D
• Chapter 12:
Simple Regression – Dependent variables: to predict
and Correlation
–dependent /
independent Dependent Variable
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Independent Variable

16. Regression Analysis
Correlation & Cause Effect?
• Review
• The relationships found by regression to be
• Chapter 12: relationships of association
Simple Regression
and Correlation
• Not necessarilly of cause and effect.
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

17. Regression Analysis
• Review
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

18. Least-squares Estimating Equation
• Review Least-squares estimating equation:
• Chapter 12:
• The dependent variable Y is determined by the independent
Simple Regression variable X
and Correlation
–dependent /
Dependent Variable
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of Y
correlation
X
I 88 ?
Independent Variable
Ŷ = a + bX

19. Least-squares Estimating Equation
• Review
Least-squares estimating equation:
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
Ŷ = a + bX
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

20. Least-squares Estimating Equation
• Review
Least-squares estimating equation:
• Chapter 12:
Simple Regression
and Correlation
xy - n x y
–dependent /
independent
variables
b= 2 2
–scatter diagrams
–regression analysis
x -nx
–Least-squares
estimating equation
–the coefficient of
determination
Y = a + bX a = Y - bX
–the coefficient of
correlation

21. Least-squares Estimating Equation
the relationship between the age of a truck and the annual repair expense?
• Review xy - nx y
b= Y = a + bX a = Y - bX
x -nx
2 2
Step 2:
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation Step 1: X=3 Y=6
–the coefficient of
determination 78 - 4 * 3 * 6
–the coefficient of
Step 4: b= 0.75 Step 6: Ŷ = 3.75 + 0.75 X
correlation 44 - 4 * 9
a = 6 - 0.75*3 = 3.75 Step 7: 6.75 = 3.75 + 0.75 * 4
Step 5:
If the city has a truck that is 4 years old,
Step 8:
the director could use the equation to predict $675 annually in repairs.

22. Least-squares Estimating Equation
• Review
To find the simple/linear regression of Personal Income (X)
and Auto Sales (Y)
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
If X=64, what about Y?
–Least-squares
estimating equation
–the coefficient of Step 1: Count the number of values. N = 5
determination
a. 4.1 Step 2: Find XY, X2 See the below table
–the coefficient of
b. 5.3
correlation
c. 6.7
d. 7.4
e. 7.5
f. 8.2

23. Least-squares Estimating Equation
• Review
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams Step 3: Find ΣX, ΣY, ΣXY, ΣX2.
–regression analysis ΣX = 311 Mean = 62.2
–Least-squares ΣY = 18.6 Mean = 3.72
estimating equation ΣXY = 1159.7
–the coefficient of
ΣX2 = 19359
determination
–the coefficient of
correlation Step 4: xy - nx y
b=
-nx
2 2
x
Substitute in the above slope formula given.
Slope(b) = 1159.7-5*62.2*3.72 = 0.19
19359-5*62.2*62.2

24. Least-squares Estimating Equation
• Review
Slope(b) = 0.19
• Chapter 12: Now, again substitute in the above intercept formula given.
Step 5:
Simple Regression
and Correlation Intercept(a) = Y - bX = 3.72- 0.19 * 62.2= -8.098
–dependent /
independent Step 6:
variables
Then substitute these values in regression equation
–scatter diagrams formula
–regression analysis Regression Equation(Ŷ) = a + bX
–Least-squares
estimating equation Ŷ = -8.098 + 0.19X
–the coefficient of
determination Regression Equation:
–the coefficient of Suppose if we want to know the
Ŷ = a + bX
correlation approximate y value for the variable X
= -8.098 + 0.19(64)
= -8.098 + 12.16 = 64. Then we can substitute the value
= 4.06
in the above equation.

25. Standard Error
• Review Standard Error:
to minimize the sum of the squares of the errors to measure the
• Chapter 12: goodness of fit of a line
Simple Regression
and Correlation
–dependent /
SE SE
independent ei = residuali
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Strong Weak
correlation correlation

26. Standard Error
• Review
• Chapter 12: ei = residuali
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

27. Coefficient of Determination
• Review Correlation Analysis:
• Chapter 12: describe the degree to which one variable is linearly
Simple Regression related to another.
and Correlation
–dependent /
independent
variables Coefficient of Determination: r 2
–scatter diagrams
–regression analysis Measure the extent, or strength, of the association that
–Least-squares
estimating equation
exists between two variables.
–the coefficient of
determination
–the coefficient of
correlation Coefficient of Correlation: r
Square root of coefficient of determination

28. Coefficient of Determination
Coefficient of Determination:
• Review
r2
• Chapter 12: • 0 ≤ r2 ≤ 1.
Simple Regression • The larger r2 , the stronger the linear relationship.
and Correlation
–dependent /
• The closer r2 is to 1, the more confident we are in
independent our prediction.
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
r 2=0.9984
–the coefficient of
determination
–the coefficient of
correlation

29. Coefficient of Determination
• Review
• Chapter 12: • 76.30% of Sales changes is explained by
Simple Regression GDP changes. The rest 23.70% is
and Correlation
–dependent /
explained by other variables.
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
r 2=0.7630
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

30. Coefficient of Correlation
• Coefficient of correlation:
Review
r
• Chapter 12: • r ≤ 0.3 Weak Correlation
Simple Regression
and Correlation
• 0.3 ≤ r ≤ 0.7 Moderate Correlation
–dependent / • r ≥ 0.7 Strong Correlation
independent
variables • r = 0.10 Perfect Correlation r 2=0.1132
–scatter diagrams
–regression analysis
–Least-squares
r =0.1064
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

31. Coefficient of Correlation
• Review • There is a positive and weak correlation
• Chapter 12:
r between GDP and Envy Rides’ annual
Simple Regression sales.
and Correlation • 11.32% of Sales changes is explained by
–dependent /
independent
r 2 GDP changes. The rest 88.68% is
variables r 2=0.1132
–scatter diagrams
explained by other variables.
–regression analysis
–Least-squares
r =0.1064
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

32. Coefficient of Correlation
• Review
• There is a positive and strong correlation
r between GDP and Envy Rides’ annual
• Chapter 12:
Simple Regression
sales.
and Correlation • 76.30% of Sales changes is explained by
–dependent /
r 2 GDP changes. The rest 23.70% is
independent
variables explained by other variables. r 2=0.7630
–scatter diagrams
–regression analysis
–Least-squares r =0.8735
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

33. Coefficient of Correlation
• Review • There is a positive and almost perfect
• Chapter 12: r correlation between GDP and Envy Rides’
Simple Regression annual sales.
and Correlation • 99.84% of Sales changes is explained by
–dependent /
independent r 2 GDP changes. The rest 8% is explained by
variables other variables.
–scatter diagrams r 2=0.9984
–regression analysis
–Least-squares
estimating equation r =0.9992
–the coefficient of
determination
–the coefficient of
correlation

34. Review
• Review
• Chapter 12:
Simple Regression
Which value of r indicates a stronger correlation than 0.40?
and Correlation
–dependent /
A. -0.30
independent B. -0.50
variables C. +0.38
–scatter diagrams D. 0
–regression analysis
–Least-squares
estimating equation If all the plots on a scatter diagram lie on a straight line, what is the
–the coefficient of standard error of estimate?
determination
A. -1
–the coefficient of
correlation B. +1
C. 0
D. Infinity

35. Review
• Review
• Chapter 12:
Simple Regression In the least squares equation, Ŷ = 10 + 20X the value of 20
and Correlation indicates
–dependent / A. the Y intercept.
independent
variables B. for each unit increase in X, Y increases by 20.
–scatter diagrams C. for each unit increase in Y, X increases by 20.
–regression analysis D. none of these.
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

36. Review
• Review
A sales manager for an advertising agency believes there is a
• Chapter 12: relationship between the number of contacts and the amount of the
Simple Regression sales. To verify this belief, the following data was collected:
and Correlation
–dependent / What is the Y-intercept of the linear equation?
independent
A. -12.201
variables
B. 2.1946
–scatter diagrams
C. -2.1946
–regression analysis
D. 12.201
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation

37. What we have learnt?
• Review
• Chapter 12:
– scatter diagrams
Simple Regression
and Correlation
– dependent / independent variables
–dependent /
independent – regression analysis
variables
–scatter diagrams – Least-squares estimating equation
–regression analysis
–Least-squares – the coefficient of determination
estimating equation
–the coefficient of – the coefficient of correlation
determination
–the coefficient of
correlation