際際滷

際際滷Share a Scribd company logo

Regression, Multiple regression in statistics

?Download as PPTX, PDF?
?
R
Rashna Asif

This presentation all about the regression and multiple regression equation of multiple regression and the most important thing is the research question of multiple regression with examples

1 of 15
Downloaded 12 times
1
Multiple Regression Presented by: Muhammad Imran Rashna Asif Sonia Javed Tahira Gillani 2
Content General purpose and Description Kinds of Research Question Limitation to Regression Analysis Fundamental Equations for Multiple Regressions 1 2 3 4 3
Multiple Regression ? Multiple regression is an extension of simple regression. ? It is a study of more than two variables. ? It is used for prediction. ? It is used when we want to predict the value of a variable based on the value of two or more other variables. ? The variable we want to predict is called the dependent variable and the variable we are using to predict the dependent variable is called independent variables. ? The dependent variable is variously known as explained variables, predictand and response variables. 4
Continue.. ? While the independent variable is known as explanatory and regressor variable. ? Here we try to predict the change in Dependent variable according to change in independent variable. ? The objective of multiple regression is to develop a prediction equation that permits the estimation of the value of the dependent variable based on the knowledge of multiple independent variables. ? It is used to estimate the relationship that exists, on the average between the dependent variable and independent variable. ? It is used to determine the effect of the each independent variable on the dependent variable, controlling the effects of all other independent variables. 5
Example 1: Predicting Final Exam Grades Assignments Midterm Multiple Regression Final 6
Example 2: ＾Does ｀ignoring problems¨ (IV1) and ｀worrying¨ (IV2) predict ｀psychological distress¨ (DV)￣ 7
Example 3: Effect of violence, stress, social support On internalizing behavior problems 8
Kinds of Research Question Research Question 1 How well do these three IVs: ? No of cigarettes / day (IV1) ? Exercise (IV2) and ? Cholesterol (IV3) predict ? CHD (Cigarettes & coronary heart disease) mortality (DV)? 9 Cigarettes Exercise CHD Mortality Cholesterol
Research Question 2 To what extent do personality factors (IVs) predict annual income (DV)? Extraversion Neuroticism Income Psychoticism 10
Research Question 3 ＾Does the # of years of formal study of psychology (IV1) and the no. of years of experience as a psychologist (IV2) predict clinical psychologists¨ effectiveness in treating mental illness (DV)?￣ Study Experience 11 Effectiveness
Limitation to Regression Analysis Multiple regression is the most powerful technique available to researchers. But powerful techniques have high demands. So, this technique requires: ? Every variable is measured at the interval-ratio level ? Independent variable does not interact with each other ? Independent variables are uncorrelated with each other ? More difficult to implement ? Best to have a lot of data points ? It involves very lengthy and complicated procedure of calculations and analysis. ? It cannot be used in case of qualitative phenomenon. 12
Fundamental Equation for Multiple Regressions ? = ?0 + ?1 ?1 + ?2 ?2 + ? ? ? ? ? + ? ? = ? ? + ? ? ? ? + ? ? ? ? + ? ? ? ? ? + ? 13 Dependent Variable Coefficients Independent Variable Number of Observations Random Error Term
Continue´ ? Dependent Variable: The single variable being predicted by the regression model ? Independent Variable: The independent variables used to predict the dependent variable. ? Coefficients (β): Values, computed by the regression tool, reflecting independent variable to dependent variable relationships. ? Random Error Term (ε): The portion of the dependent variable that isn¨t explained by the model; the model under and over predictions. 14
15

More Related Content

Regression, Multiple regression in statistics

  • 1. 1
  • 2. Multiple Regression Presented by: Muhammad Imran Rashna Asif Sonia Javed Tahira Gillani 2
  • 3. Content General purpose and Description Kinds of Research Question Limitation to Regression Analysis Fundamental Equations for Multiple Regressions 1 2 3 4 3
  • 4. Multiple Regression ? Multiple regression is an extension of simple regression. ? It is a study of more than two variables. ? It is used for prediction. ? It is used when we want to predict the value of a variable based on the value of two or more other variables. ? The variable we want to predict is called the dependent variable and the variable we are using to predict the dependent variable is called independent variables. ? The dependent variable is variously known as explained variables, predictand and response variables. 4
  • 5. Continue.. ? While the independent variable is known as explanatory and regressor variable. ? Here we try to predict the change in Dependent variable according to change in independent variable. ? The objective of multiple regression is to develop a prediction equation that permits the estimation of the value of the dependent variable based on the knowledge of multiple independent variables. ? It is used to estimate the relationship that exists, on the average between the dependent variable and independent variable. ? It is used to determine the effect of the each independent variable on the dependent variable, controlling the effects of all other independent variables. 5
  • 6. Example 1: Predicting Final Exam Grades Assignments Midterm Multiple Regression Final 6
  • 7. Example 2: ＾Does ｀ignoring problems¨ (IV1) and ｀worrying¨ (IV2) predict ｀psychological distress¨ (DV)￣ 7
  • 8. Example 3: Effect of violence, stress, social support On internalizing behavior problems 8
  • 9. Kinds of Research Question Research Question 1 How well do these three IVs: ? No of cigarettes / day (IV1) ? Exercise (IV2) and ? Cholesterol (IV3) predict ? CHD (Cigarettes & coronary heart disease) mortality (DV)? 9 Cigarettes Exercise CHD Mortality Cholesterol
  • 10. Research Question 2 To what extent do personality factors (IVs) predict annual income (DV)? Extraversion Neuroticism Income Psychoticism 10
  • 11. Research Question 3 ＾Does the # of years of formal study of psychology (IV1) and the no. of years of experience as a psychologist (IV2) predict clinical psychologists¨ effectiveness in treating mental illness (DV)?￣ Study Experience 11 Effectiveness
  • 12. Limitation to Regression Analysis Multiple regression is the most powerful technique available to researchers. But powerful techniques have high demands. So, this technique requires: ? Every variable is measured at the interval-ratio level ? Independent variable does not interact with each other ? Independent variables are uncorrelated with each other ? More difficult to implement ? Best to have a lot of data points ? It involves very lengthy and complicated procedure of calculations and analysis. ? It cannot be used in case of qualitative phenomenon. 12
  • 13. Fundamental Equation for Multiple Regressions ? = ?0 + ?1 ?1 + ?2 ?2 + ? ? ? ? ? + ? ? = ? ? + ? ? ? ? + ? ? ? ? + ? ? ? ? ? + ? 13 Dependent Variable Coefficients Independent Variable Number of Observations Random Error Term
  • 14. Continue´ ? Dependent Variable: The single variable being predicted by the regression model ? Independent Variable: The independent variables used to predict the dependent variable. ? Coefficients (β): Values, computed by the regression tool, reflecting independent variable to dependent variable relationships. ? Random Error Term (ε): The portion of the dependent variable that isn¨t explained by the model; the model under and over predictions. 14
  • 15. 15