0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Regression

1,276

Published on

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

Views
Total Views
1,276
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
92
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. UNIT III REGRESSION
• 2. Meaning &#xF0A8; The dictionary meaning of regression is &#x201C;the act of returning or going back&#x201D;; &#xF0A8; First used in 1877 by Francis Galton; &#xF0A8; Regression is the statistical tool with the help of which we are in a position to estimate (predict) the unknown values of one variable from the known values of another variable; &#xF0A8; It helps to find out average probable change in one variable given a certain amount of change in another;
• 3. Importance
• 4. Regression lines &#xF0A8; For two variables X and Y, we will have two regression lines: 1. Regression line X on Y gives values of Y for given values of X; 2. Regression line Y on X gives values of X for given values of Y;
• 5. Regression Equation &#xF0A8; Regression equations are algebraic expressions of regression lines; Y on X Regression equation expressed as Y=a+bX Y is dependent variable X is independent variable &#x201E;a&#x201F; &amp; &#x201E;b&#x201F; are constants/parameters of line &#x201E;a&#x201F; determines the level of fitted line (i.e. distance of line above or below origin) &#x201E;b&#x201F; determines the slope of line (i.e change in Y for unit change in X)
• 6. &#xF0A8; Regression equations are algebraic expressions of regression lines; X on Y Regression equation expressed as X=a+bY X is dependent variable Y is independent variable &#x201E;a&#x201F; &amp; &#x201E;b&#x201F; are constants/parameters of line &#x201E;a&#x201F; determines the level of fitted line (i.e. distance of line above or below origin) &#x201E;b&#x201F; determines the slope of line (i.e change in Y for unit change in X)
• 7. Method of Least Square &#xF0A8; Constant &#x201C;a&#x201D; &amp; &#x201C;b&#x201D; can be calculated by method of least square; &#xF0A8; The line should be drawn through the plotted points in such a manner that the sum of square of the vertical deviations of actual Y values from estimated Y values is the least i.e. &#x2211;(Y-Ye)2 should be minimum; &#xF0A8; Such a line is known as line of best fit; &#xF0A8; with algebra &amp; calculus: For Y on X For X on Y &#x2211;Y=Na+b &#x2211;X &#x2211;X=Na+b &#x2211;Y &#x2211;XY=a &#x2211;X + b &#x2211;X2 &#x2211;XY=a &#x2211;Y + b &#x2211;Y2
• 8. Multiple Regression &#xF0A8; When we use more than one independent variable to estimate the dependent variable in order to increase the accuracy of the estimate; the process is called multiple regression analysis. &#xF0A8; It is based on the same assumptions &amp; procedure that are encountered using simple regression. &#xF0A8; The principal advantage of multiple regression is that it allows us to use more of the information available to us to estimate the
• 9. Estimating equation describing relationship among three variables Y= a+b1X1+b2X2 &#xF0A8; where, Y = estimated value corresponding to the dependent variable &#xF0A8; a= Y intercept &#xF0A8; b1 and b2 = slopes associated with X1 and X2, respectively &#xF0A8; X1 and X2 = values of the two independent variables
• 10. Normal Equations: &#xF0A8; we use three equations (which statistician call the &#x201C;normal equation&#x201D;) to determine the values of the constants a, b1 and b2 &#xF0A8; &#x2211;Y=Na+b1&#x2211;X1 + b2&#x2211;X2 &#xF0A8; &#x2211;X1Y=a &#x2211;X1 + b1 &#x2211;X1 2 + b2&#x2211;X1 X2 &#xF0A8; &#x2211;X2Y=a &#x2211;X2 + b2 &#x2211;X2 2 + b1&#x2211;X1 X2
• 11. Difference between regression &amp; correlation &#xF0A8; Correlation coefficient (r) between x &amp; y is a measure of direction &amp; degree of linear relationship between x &amp; y; &#xF0A8; It does not imply cause &amp; effect relationship between the variables. &#xF0A8; It indicates the degree of association &#xF0A8; bxy &amp; byx are mathematical measures expressing the average relationship between the two variables &#xF0A8; It indicates the cause &amp; effect relationship between variables. &#xF0A8; It is used to forecast the nature of dependent variable when the value of independent variable is Correlation Regression