Download presentation

2
**Sleeping and Happiness**

Hours slept (X) Happiness (Y) Pam 8 7 Jim 9 Dwight 5 4 Michael 6 Meredith You are interested in the relationship between hours slept and happiness. 1) Make a scatter plot 2) Guess the correlation 3) Guess and draw the location of the regression line

3
. . . . . r = .76

4
**Remember this: Statistics Needed**

Need to find the best place to draw the regression line on a scatter plot Need to quantify the cluster of scores around this regression line (i.e., the correlation coefficient)

5
**Regression allows us to predict!**

. . . . .

6
**Straight Line Y = mX + b Where:**

Y and X are variables representing scores m = slope of the line (constant) b = intercept of the line with the Y axis (constant)

7
Excel Example

8
That’s nice but How do you figure out the best values to use for m and b ? First lets move into the language of regression

9
**Straight Line Y = mX + b Where:**

Y and X are variables representing scores m = slope of the line (constant) b = intercept of the line with the Y axis (constant)

10
**Regression Equation Y = a + bX Where:**

Y = value predicted from a particular X value a = point at which the regression line intersects the Y axis b = slope of the regression line X = X value for which you wish to predict a Y value

11
**Practice Y = -7 + 2X What is the slope and the Y-intercept?**

Determine the value of Y for each X: X = 1, X = 3, X = 5, X = 10

12
**Practice Y = -7 + 2X What is the slope and the Y-intercept?**

Determine the value of Y for each X: X = 1, X = 3, X = 5, X = 10 Y = -5, Y = -1, Y = 3, Y = 13

13
**Finding a and b Uses the least squares method Minimizes Error**

Error = Y - Y (Y - Y)2 is minimized

14
. . . . .

15
**. . . . . Error = Y - Y (Y - Y)2 is minimized Error = 1 Error = .5**

16
**Finding a and b Ingredients r value between the two variables**

Sy and Sx Mean of Y and X

17
**b = b r = correlation between X and Y SY = standard deviation of Y**

SX = standard deviation of X

18
a a = Y - bX Y = mean of the Y scores b = regression coefficient computed previously X = mean of the X scores

19
**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41**

20
**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41**

21
**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41**

b =

22
**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41**

b = .88 1.50 1.41

23
**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41 b = 1.5**

a = Y - bX

24
**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41 b = 1.5**

0.1 = (1.50)3.0

25
Regression Equation Y = a + bX Y = (1.5)X

26
Y = (1.5)X . . . . .

27
Y = (1.5)X X = 1; Y = 1.6 . . . . . .

28
Y = (1.5)X X = 5; Y = 7.60 . . . . . . .

29
Y = (1.5)X . . . . . . .

Similar presentations

OK

5-7: Scatter Plots & Lines of Best Fit. What is a scatter plot? A graph in which two sets of data are plotted as ordered pairs When looking at the.

5-7: Scatter Plots & Lines of Best Fit. What is a scatter plot? A graph in which two sets of data are plotted as ordered pairs When looking at the.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on road signs in india Ppt on bank management system in java Miracles in the bible ppt on how to treat Ppt on projectile motion Ppt on index numbers pdf Ppt on rabindranath tagore poems Ppt on role of mass media in education Ppt on means of transport free download Ppt online open house Ppt on number system for class 10th