Regression with Examples and Question and Its Types
- 1. Regression
- 2. Regression ⢠Regression is a statistical method used to understand and quantify the relationship between two or more variables. ⢠It helps us predict one variable based on the values of other variables. It mean that one variable are Independent and other variable are dependent,. ⢠Simple words, In regression, one thing impact on other but other not impact on one.
- 3. Examples of Regression ⢠The Example of regression are the relationship between the Temperature and the sales of ice cream in a particular area. ⢠Ice-cream is a dependent variable and Temperature in independent variable and simple way to predict ice-cream sales based on the temperature. ⢠If the temperature increase, the ice-cream sales increase and if the temperature is low, the ice-cream sales will be low.
- 4. Dependent Variable ⢠The dependent variable is what you're trying to find out or measure. ⢠It "depends" on other factors. It's like the answer or the result. ďą Example: ⢠If you're studying how the amount of sunlight affects plant growth, the plant growth is the dependent variable. It depends on the amount of sunlight.
- 5. Independent Variable ⢠The independent variable is what you change or control in an experiment. ďą Example: ⢠How the amount of sunlight affects plant growth: ⢠Dependent Variable: Plant growth ⢠Independent Variable: Amount of sunlight
- 6. Cont.âŚ. ⢠The independent variable is the amount of sunlight because it's what you are changing or manipulating to observe its effect on the dependent variable, which is plant growth.
- 7. Types of Regression ⢠Two Main Types of Regression are; ⢠Linear Regression ⢠Multiple Regression
- 8. Linear Regression ⢠Simple linear regression has only one x and one y variable. ⢠Linear regression is like drawing a straight line through a bunch of points on a graph. ⢠It helps us understand the average relationship between two things. ⢠For Example, the number of hours students study and their exam scores.
- 9. Multiple Regression ⢠Multiple linear regression uses two or more independent variables to predict the outcome ⢠Multiple regression is like extending linear regression when there are more than one variables influencing the outcome. ⢠Multiple linear regression has one y and two or more x variables.
- 10. Example ⢠For Example; Predicting House Price ⢠Imagine you want to predict the price of a house. Instead of just looking at one factor like the size of the house, you consider multiple factors: ⢠Size of the House (in square feet) ⢠Number of Bedrooms
- 11. Cont.⌠⢠Distance to the City Center (in miles) ⢠The price of a house depends on its size, the number of bedrooms, and the distance to the city center."
- 12. Regression Equation ⢠A regression equation is a equation that best describes the linear relationship between the two variables. ⢠It is expressed by the means of an equation of the form: ďź X on Y ďź Y on X
- 13. Regression Equation ⢠The Regression equation of X on Y is X=a + bY ⢠Y = Independent Variable ⢠a = intercept ⢠b = regression coefficient ⢠X = dependent Variable
- 14. Cont.⌠⢠The Regression equation of Y on X is Y=a + bX ⢠Y = Dependent Variable ⢠a = intercept ⢠b = regression coefficient ⢠X = Independent Variable
- 15. Formula On X on Y x = a +by a = -b b =
- 16. Least Square Method ⢠The Regression equation of Y on X is Y=a + Bx Where ⢠Y = Dependent Variable ⢠a = intercept ⢠b = regression coefficient ⢠X = Independent Variable
- 17. Question ⢠From the following data obtain the two regression equations using the method of least squares.
- 18. X Y 3 10 5 12 6 15 9 18 10 20 12 22 15 27 20 30 22 32 28 34
- 19. Solution ⢠Find Regression Equation on X on Y X = a + by a = -b b =
- 20. 3 10 9 100 30 5 12 25 144 60 6 15 36 225 90 9 18 81 324 162 10 20 100 400 200 12 22 144 484 264 15 27 225 729 405 20 30 400 900 600 22 32 484 1024 704 28 34 784 1156 952 2288 5486 3467
- 21. b = ? b = b = = 0.93 a = ? a = = = = = = 22 a = a = a = -7.46
- 22. So put the values in Regression Line X on Y X = a + by And Regression line is X = -7.46 + 0.9y