![First, we solve for the regression coefficient (b1):
b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2]
b1 = 470/730
b1 = 0.644
Once we know the value of the regression coefficient
(b1), we can solve for the regression slope (b0):
b0 = y - b1 * x
b0 = 77 - (0.644)(78)
b0 = 26.768
Therefore, the regression equation is:
ŷ = 26.768 + 0.644x .
To conduct a regression analysis, we need to solve for b0
and b1. Computations are shown below.
Once you have the regression equation, using it is a
snap. Choose a value for the independent variable (x),
perform the computation, and you have an estimated
value (ŷ) for the dependent variable.
In our example, the independent variable is the student's
score on the aptitude test. The dependent variable is the
student's statistics grade. If a student made an 80 on the
aptitude test, the estimated statistics grade (ŷ) would be:
ŷ = b0 + b1x
ŷ = 26.768 + 0.644x = 26.768 + 0.644 * 80
ŷ = 26.768 + 51.52 = 78.288](https://image.slidesharecdn.com/regressionanalysis-181215173332/85/Regressionanalysis-10-320.jpg)
Regressionanalysis
- 2. Audience SDSF, DAVV MBA (Business Analytics) Submitted to: Dr. Dipshikha Agarwal Submitted by: Manokamna Kochar
- 3. What is regression analysis? Regression analysis is a technique for measuring the relationship between two interval- or ratio-level variables. The regression framework is at the heart of empirical social and political science research. Regression analysis acts as a statistical surrogate for controlled experiments, and can be used to make causal inferences.
- 4. What is regression analysis? The basis for this is to find the relationship between the dependent and independent variables. The value of dependent variable is of most importance to researchers and depends on the value of other variables. Independent variable is used to explain the variation in the dependent variable. It can be classified into two types − Simple regression − One independent variable Multiple regression − Several independent variables
- 5. Simple Regression Following are the steps to build up regression analysis 1.Specify the regression model 2.Obtain data on variables 3.Estimate the quantitative relationships 4.Test the statistical significance of the results 5.Usage of results in decision-making
- 6. Procedure
- 7. Method of Ordinary Least Squares OLS 1. Ordinary least square method is designed to fit a line through a scatter of points is such a way that the sum of the squared deviations of the points from the line is minimized. It is a statistical method. Usually Software packages perform OLS estimation. Formula for simple regression is − Y = a + bX + u Y= dependent variable X= independent variable a= intercept b= slope u= random factor
- 8. Properties of the Ordinary Least Squares OLS A1. The linear regression model is “linear in parameters.” A2. There is a random sampling of observations. A3. The conditional mean should be zero. A4. There is no multi-collinearity (or perfect collinearity). A5. Spherical errors: There is homoscedasticity and no auto-correlation A6: Optional Assumption: Error terms should be normally distributed.
- 9. How to find regression equation ? In the table below, the xi column shows scores on the aptitude test. Similarly, the yi column shows statistics grades. The last two columns show deviations scores - the difference between the student's score and the average score on each test. The last two rows show sums and mean scores that we will use to conduct the regression analysis.
- 10. First, we solve for the regression coefficient (b1): b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2] b1 = 470/730 b1 = 0.644 Once we know the value of the regression coefficient (b1), we can solve for the regression slope (b0): b0 = y - b1 * x b0 = 77 - (0.644)(78) b0 = 26.768 Therefore, the regression equation is: ŷ = 26.768 + 0.644x . To conduct a regression analysis, we need to solve for b0 and b1. Computations are shown below. Once you have the regression equation, using it is a snap. Choose a value for the independent variable (x), perform the computation, and you have an estimated value (ŷ) for the dependent variable. In our example, the independent variable is the student's score on the aptitude test. The dependent variable is the student's statistics grade. If a student made an 80 on the aptitude test, the estimated statistics grade (ŷ) would be: ŷ = b0 + b1x ŷ = 26.768 + 0.644x = 26.768 + 0.644 * 80 ŷ = 26.768 + 51.52 = 78.288
- 11. Thankyou