Regression is a statistical method used to determine the relationship between variables and make predictions, where one variable (dependent) is predicted from the value of others (independents). It measures how well observed outcomes are replicated by the model, and is used in finance and other fields to understand how one factor impacts another. Examples show regression output including R-Square, ANOVA, coefficients, and correlation between variables ranging from -1 to +1 to indicate the strength and direction of relationships.

1. What Is Regression?
Regression is a statistical measurement used in finance, investing, and other disciplines that
attempts to determine the strength of the relationship between one dependent variable (usually
denoted by Y) and a series of other changing variables (known as independent variables).
OR
Regression is a statistical method used in finance and other fields to make predictions based on
observed values. It is a measure of how correlated a group of actual observations are to a model’s
predictions.

2. Examples:
R-Square= 6.5 % (Total variation in the dependent variable explained by independent
variable)
Anova is Significant (P<0.05), So research model is fit.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .254a .065 .058 .69080
a. Predictors: (Constant), Marketing
b. Outcome: Sales
ANOVAa
Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression 5.071 1 5.071 10.626 .001b
Residual 73.489 154 .477
Total 78.560 155
a. Dependent Variable: Sales
b. Predictors: (Constant), Marketing

3. Coefficients
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 4.242 .228 18.606 .000
Marketing .240 .074 .254 3.260 .001
a. Dependent Variable: Sales
b. Independent Variable: Marketing
Fluctuation of positive value of .240 with one unit change in the
independent variable

4. Example 2:
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .511a .261 .254 .70834
ANOVAa
Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression 18.460 1 18.460 36.791 .000b
Residual 52.182 104 .502
Total 70.642 105

5. Coefficients
Model Unstandardized
Coefficients
Standardize
d
Coefficients
t Sig.
B Std. Error Beta
1
(Constant) 1.643 .296 5.561 .000
independent .454 .075 .511 6.066 .000

6. Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .287a .083 .061 .63663
ANOVAa
Model Sum of
Squares
df Mean
Square
F Sig.
1
Regression 3.139 2 1.570 3.873 .025b
Residual 34.856 86 .405
Total 37.995 88
Coefficients
Model Unstandardized
Coefficients
Standardiz
ed
Coefficient
s
t Sig. Collinearity
Statistics
B Std. Error Beta Toleran
ce
VIF
1
(Constant) 4.497 .208 21.616 .000
Independent -.067 .106 -.070 -.633 .528 .872 1.147

7. Correlation:
Degree and type of relationship between any two or more quantities (variables) in which they
vary together over a period; for example, variation in the level of expenditure or savings with
variation in the level of income. A positive correlation exists where the high values of one
variable are associated with the high values of the other variable(s). A 'negative correlation'
means association of high values of one with the low values of the other(s). Correlation can vary
from +1 to -1. Values close to +1 indicate a high-degree of positive correlation, and values close
to -1 indicate a high degree of negative correlation.
Correlation is usually defined as a measure of the linear relationship between two quantitative
variables (e.g., height and weight). ... An example of positive correlation may be that the more
you exercise, the more calories you will burn.

8. • Correlation is used to test relationships between quantitative variables or categorical variables.
In other words, it’s a measure of how things are related. The study of how variables are
correlated is called correlation analysis.
Range: -1 to +1
Examples:
• Your caloric intake and your weight.
• Your eye color and your relatives’ eye colors.
• The amount of time your study and your GPA.

9. Examples:
r=0.358 (Positive and low to moderate correlation)
p=0.001 (Significant relationship as P<0.05)
Motivation Performance
Motivation
Pearson
Correlation
1 .358
Sig. (2-tailed) .001
N 89 89
Performance
Pearson
Correlation
.358 1
Sig. (2-tailed) .001
N 89 89

10. Salary Buying
Salary
Pearson Correlation 1 .420**
Sig. (2-tailed) .000
N 106 106
Buying
Pearson Correlation .420** 1
Sig. (2-tailed) .000
N 106 106