1. Quantitative Methods
Simple Regression

2. Multiple Regression Simple Regression Model Least Squares Method
Coefficient of Determination
Model Assumptions
Testing for Significance
Using the Estimated Regression Equation
for Estimation and Prediction

3. The Simple Regression Model
y = 0 + 1x1 + 
The Estimated Simple Regression Equation
y = b0 + b1x1 ^

4. The Least Squares Method
Least Squares Criterion
Computation of Coefficients’ Values
The formulas for the regression coefficients b0, b1
b1 = n Σ x y - Σx Σy /nΣx2 – (Σx)2
b0 = ¯y - b1 ¯x or
b1 = COV(X,Y)/S2x
b1 = r (Sy/Sx)
A Note on Interpretation of Coefficients
b1 represents an estimate of the change in y corresponding to a one-unit change in x. It is known as regression coefficient ^

5. The Coefficient of Determination
Relationship Among SST, SSR, SSE
SST = SSR + SSE
Coefficient of Determination
R 2 = SSR/SST
It measures extent of variation in Y explained by the regression equation ^ ^

6. The Coefficient of Determination
Coefficient of Determination R2:It is the square of correlation coefficient r & it measures strength of association in regression.

7. Model Assumptions Assumptions About the Error Term 
The error  is a random variable with mean of zero.
The variance of  , denoted by 2
The values of  are independent.
The error  is a normally distributed random variable

8. Testing for Significance: F Test
Hypotheses
H0: 1 = 0
Ha: 1 ≠0
Test Statistic
F = MSR/MSE
Rejection Rule
Reject H0 if F > F
where F is based on an F distribution with 1d.f. in the numerator and n – 2 d.f. in the denominator.

9. Testing for Significance: t Test
Hypotheses
H0: 1= 0
Ha: 1 = 0
Test Statistic
Rejection Rule
Reject H0 if t < -tor t > t
where t is based on a t distribution with
n - p - 1 degrees of freedom.

10. Using the Estimated Regression Equation for Estimation and Prediction
The procedures for estimating and predicting an individual value of y in simple regression
We substitute the given values of x into the estimated regression equation and use the corresponding value of y as the point estimate. . ^