The document discusses correlation, regression analysis, and an example analysis. It defines correlation as a measure of the strength of association between two variables. Regression analysis establishes a mathematical relationship between variables to predict outcomes. The example analyzes the correlation between residents' duration of residence in a city and their attitude toward the city, finding a strong positive correlation. It then performs a bivariate regression to model this relationship mathematically.

1. Correlation and Regression
10/13/14 1

2. Product Moment Correlation
• The product moment correlation, r, summarizes the
strength of association between two metric (interval or
ratio scaled) variables, say X and Y.
• It is an index used to determine whether a linear or
straight-line relationship exists between X and Y.
• As it was originally proposed by Karl Pearson, it is
also known as the Pearson correlation coefficient.
It is also referred to as simple correlation, bivariate
correlation, or merely the correlation coefficient.
• A correlation is a single number that describes the
degree of relationship between two variables. (http://
www.socialresearchmethods.net/kb/statcorr.php )
10/13/14 2

3. SPSS
• Is there any correlation/association
between attitude toward the city and
duration of residence?
H0 : There is no association/ correlation
between duration of residence and attitude
toward the city
H1 : There is an association/ correlation
between between duration of residence
and attitude toward the city
10/13/14 3

4. Tab le 17.1
Respondent No Attitude Toward
the City
Duration of
Residence
Importance
Attached to
Weather
1 6 10 3
2 9 12 11
3 8 12 4
4 3 4 1
5 10 12 11
6 4 6 1
7 5 8 7
8 2 2 4
9 11 18 8
10 9 9 10
11 10 17 8
12 2 2 5
10/13/14 4

5. Descriptive Statistics
Mean Std. Deviation N
6,58 3,32 12
9,33 5,26 12
Attitude toward the city
Duration of residence
Correlations
1,000 ,936**
10/13/14 5
, ,000
120,917 179,667
10,992 16,333
12 12
,936** 1,000
,000 ,
179,667 304,667
16,333 27,697
12 12
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Attitude toward the city
Duration of residence
Attitude
toward the city
Duration of
residence
Correlation is significant at the 0.01 **. level (2-tailed).

6. Correlation Coefficient
n
S (Xi – X) (Yi – Y)
i=1
r = = COVxy / SxSy
n n
S (Xi – X)2 S (Yi – Y)2
i=1 i=1
10/13/14 6

7. Y X1 X2
r = (179.6668) / [(304/6669)(120.9168) = 0.9361
The respondent’s duration of residence in the city
is strongly associated with attitude toward the city
10/13/14 7

8. city
the toward Attitude N = 2 1 1 1 1 1 3 1 1
2 4 6 8 9 10 12 17 18 10/13/14 8
Duration of residence
12
10
8
6
4
2
0

9. • Analyze > correlate > bivariate
– Options : - means and standar deviations
- cross product deviations and covariances
• Graphs > box plot > simple > define >ok
10/13/14 9

10. Regression Analysis
• Regression analysis is a statistical procedure for
analyzing associative relationship between a
metric dependent variable and one or more
metric independent variables.
• Independent variable affect dependent variable
10/13/14 10

11. Regression Analysis can be used in
the following ways:
1. Determine whether the independent variables
explain a significant variation in the dependent
variable: whether a relationship exists.
2. Determine how much of the variation in the
dependent variable can be explained by the
independent variables: strength of the relationship.
3. Determine the structure or form of the relationship:
the mathematical equation relating the independent
and dependent variables.
4. Predict the values of the dependent variables.
5. Control for other independent variables when
evaluating the contributions of specific variable or
set of variables.
10/13/14 11

12. Bivariate Regression
• Bivariate regression is a procedure for deriving a
mathematical relationship, in the form of an
equation, between a single metric dependent
variable and a single metric independent
variable.
• Bivariate regression example in marketing:
– Can variation in sales be explained in terms of
variation in advertising expenditures? What is the
structure and form of this relationship, can it be
modeled mathematically by an equation describing a
straight line.
10/13/14 12

13. Multiple Regression
The general form of the multiple regression model
is as follows:
Y = b0 + b1X1 + b2X2 + b3X3+ . . . + bkXk + e
which is estimated by the following equation:
Y
= a + b1X1 + b2X2 + b3X3+ . . . + bXkk
As before, the coefficient a represents the intercept,
but the b's are now the partial regression coefficients.
10/13/14 13

14. Statistics Associated with
Multiple Regression
• Adjusted R2. R2, coefficient of multiple determination, is
adjusted for the number of independent variables and the
sample size to account for the diminishing returns. After
the first few variables, the additional independent
variables do not make much contribution.
• Coefficient of multiple determination. The strength of
association in multiple regression is measured by the
square of the multiple correlation coefficient, R2, which is
also called the coefficient of multiple determination.
• F test. The F test is used to test the null hypothesis that
the coefficient of multiple determination in the population,
R2
pop, is zero. This is equivalent to testing the null
hypothesis. The test statistic has an F distribution with k
and (n - k - 1) degrees of freedom.
10/13/14 14

15. Model Summary
R R Square
Adjusted
R Square
Std. Error of
the Estimate
Change Statistics
R Square
Change F Change df1 df2 Sig. F Change
,975a ,951 ,942 ,762 ,951 105,826 2 11 ,000
Model
1
Predictors: (Constant), a. PRICE, QUALITY
ANOVAb
Sum of
Squares df Mean Square F Sig.
122,831 2 61,415 105,826 ,000a
6,384 11 ,580
129,214 13
Regression
Residual
Total
Model
1
a. Predictors: (Constant), PRICE, QUALITY
b. Dependent Variable: PREFEREN
Coefficientsa
Unstandardized
Coefficients
B Std. Error
Standardized
Coefficients
Beta
t Sig.
,535 ,471 1,136 ,280
,976 ,097 ,798 10,096 ,000
,251 ,071 ,278 3,522 ,005
(Constant)
QUALITY
PRICE
Model
1
a. Dependent Variable: PREFEREN
10/13/14 15