Download presentation

Presentation is loading. Please wait.

Published byElmer Powell Modified over 2 years ago

1
Regression Analysis Simple Regression

2
y = mx + b y = a + bx

3
where: y dependent variable (value depends on x) a y-intercept (value of y when x = 0) b slope (rate of change in ratio of delta y divided by delta x) x independent variable

4
Assumptions Linearity Independence of Error Homoscedasticity Normality

5
Linearity The most fundamental assumption is that the model fits the situation [i.e.: the Y variable is linearly related to the value of the X variable].

6
Independence of Error The error (residual) is independent for each value of X. [Residual = observed - predicted]

7
Homoscedasticity The variation around the line of regression constant for all values of X.

8
Normality T he values of Y be normally distributed at each value of X.

9
Diagnostic Checking u Linearity u Independence u Examine scatter plot of residuals versus fitted [Y hat ] for evidence of nonlinearity u Plot residuals in time order and look for patterns

10
Diagnostic Checking u Homoscedasticity u Normality u Examine scatter plots of residuals versus fitted [Y hat ] and residuals vs time order and look for changing scatter. u Examine histogram of residuals. Look for departures from normal curve.

11
Goal Develop a statistical model that can predict the values of a dependent (response) variable based upon the values of the independent (explanatory) variable(s).

12
Goal

13
Simple Regression quantitative quantitative A statistical model that utilizes one quantitative independent variable “X” to predict the quantitative dependent variable “Y.”

14
Mini-Case Since a new housing complex is being developed in Carmichael, management is under pressure to open a new pie restaurant. Assuming that population and annual sales are related, a study was conducted to predict expected sales.

15
Mini-Case (Descartes Pie Restaurants)

16
Mini-Case u What preliminary conclusions can management draw from the data? u What could management expect sales to be if population of the new complex is approximately 18,000 people?

17
Scatter Diagrams u The values are plotted on a two- dimensional graph called a “scatter diagram.” u Each value is plotted at its X and Y coordinates.

18
Scatter Plot of Pieshop

19
Types of Models No relationship between X and Y Positive linear relationship Negative linear relationship

20
Method of Least Squares u The straight line that best fits the data. u Determine the straight line for which the differences between the actual values (Y) and the values that would be predicted from the fitted line of regression (Y-hat) are as small as possible.

21
Measures of Variation Explained Unexplained Total

22
Explained Variation Sum of Squares (Y hat - Y bar ) 2 due to Regression [SSR]

23
Unexplained Variation Sum of Squares (Y obs - Y hat ) 2 Error [SSE]

24
Total Variation Sum of Squares (Y obs - Y bar ) 2 Total [SST]

25
H0:H0: There is no linear relationship between the dependent variable and the explanatory variable

26
Hypotheses H 0 : = 0 H 1 : 0 or H 0 : No relationship exists H 1 : A relationship exists

27
Analysis of Variance for Regression

28
Standard Error of the Estimate s y.x - the measure of variability around the line of regression

29
Relationship When null hypothesis is rejected, a relationship between Y and X variables exists.

30
Coefficient of Determination R 2 measures the proportion of variation that is explained by the independent variable in the regression model. R 2 = SSR / SST

31
Confidence interval estimates »True mean YX »Individual Y-hat

32
Pieshop Forecasting

33
Coefficient of Sanity

34
Diagnostic Checking u H 0 retain or reject {Reject if p-value 0.05} u R 2 (larger is “better”) u s y.x (smaller is “better”)

35
Analysis of Variance for Regression for Pieshop

36
Coefficient of Determination R 2 = SSR / SST = 90.27 % thus, 90.27 percent of the variation in annual sales is explained by the population.

37
Standard Error of the Estimate s y.x = 13.8293 with SSE = 1,530.0

38
Regression Analysis [Simple Regression] *** End of Presentation *** Questions?

Similar presentations

OK

Regression Analysis Once a linear relationship is defined, the independent variable can be used to forecast the dependent variable. Y ^ = bo + bX bo is.

Regression Analysis Once a linear relationship is defined, the independent variable can be used to forecast the dependent variable. Y ^ = bo + bX bo is.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on marie curie's accomplishments Ppt on male reproductive system of human Ppt on current account deficit means Ppt on hard gelatin capsule shells Ppt on us health insurance Download ppt on say no to crackers Ppt on conceptual artist Ppt on resources of water Ppt on computer science projects Ppt on content addressable memory cisco