- 71 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' The plan' - preston-hays

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

The plan

- Practice – Correlation
- A straight line
- A regression equation
- Practice!
- A quicker way to compute a correlation

Practice

- Interpret the following:
- 1) The correlation between vocational-interest scores at age 20 and at age 40 was .70.
- 2) Age and IQ is correlated -.16.
- 3) The correlation between IQ and family size is -.30.
- 4) The correlation between sexual promiscuity and dominance is .32.
- 5) In a sample of males happiness and height is correlated .11.

Sleeping and Happiness

- 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

Sleeping and Happiness

- 4) Compute the correlation
- Hours Slept
M = 7.0

SD = 1.4

- Happiness
M = 6.8

SD = 1.7

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)

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)

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

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)

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

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

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

Finding a and b

- Uses the least squares method
- Minimizes Error
Error = Y - Y

(Y - Y)2 is minimized

(Y - Y)2 is minimized

.

Error = 1

.

Error = .5

.

.

Error = -1

.

Error = 0

Error = -.5

Finding a and b

- Ingredients
- r value between the two variables
- Sy and Sx
- Mean of Y and X

a

a = Y - bX

Y = mean of the Y scores

b= regression coefficient computed previously

X = mean of the X scores

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

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

b =

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

a = Y - bX

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

0.1 = 4.6 - (1.50)3.0

Mean Y = 14.50; Sy = 4.43Mean X = 6.00; Sx= 2.16 r = -.57

Mean Y = 14.50; Sy = 4.43Mean X = 6.00; Sx= 2.16 r = -.57

b =

Mean Y = 14.50; Sy = 4.43Mean X = 6.00; Sx= 2.16 b = -1.17

a = Y - bX

Mean Y = 14.50; Sy = 4.43Mean X = 6.00; Sx= 2.16 b = -1.17

21.52= 14.50 - (-1.17)6.0

Mean Y = 108.57; Sy = 20.30Mean X = 4.29; Sx= 1.03

Practice

- How much money would likely be earned if an advertiser spent $2,000 (i.e., x = 2)?
- How much money would likely be earned if an advertiser spent $10,000 (i.e., x = 10)?

Blanched Formula

3360

14.5

(4.29) (108.57)

7

.68 =

2.16

4.43

(1.03) (20.30)

XY = 3360

X = 4.29

Y = 108.57

Sx = 1.03

Sy = 20.30

N = 7

Mean Y = 108.57; Sy = 20.30Mean X = 4.29; Sx= 1.03 r = .68

b =

Mean Y = 108.57; Sy = 20.30Mean X = 4.29; Sx= 1.03 b = 13.40

a = Y - bX

Mean Y = 108.57; Sy = 20.30Mean X = 4.29; Sx= 1.03 b = 13.40

51.08 = 108.57 - (13.40)4.29

Y = 51.08 + (13.40)X

- How much money would likely be earned if an advertiser spent $2,000?
- How much money would likely be earned if an advertiser spent $10,000?

Y = 51.08 + (13.40)X

- How much money would likely be earned if an advertiser spent $2,000?
- 77.88 = 51.08 + (13.40)2
- $77, 880

Y = 51.08 + (13.40)X

- How much money would likely be earned if an advertiser spent $10,000?
- 185.08 = 51.08 + (13.40)10
- $185,080

Blanched Formula

- Good way to calculate r if the means and standard deviations are already provided.
- It is very time consuming to calculate these statistics if they are not already provided
- If means and standard deviations are not given, use the raw-score formula

Step 6: Plug in values

(5)

84

15

23

r =

(5)

55

(5)

135

15

23

Y = 23 Y2 = 135

X = 15 X2 = 55

XY = 84 N = 5

Step 7: Solve!

(5)

84

15

23

r =

(5)

55

(5)

135

15

23

Y = 23 Y2 = 135

X = 15 X2 = 55

XY = 84 N = 5

Step 7: Solve!

(5)

84

15

23

r =

(5)

55

(5)

135

23

225

529

225

Y = 23 Y2 = 135

X = 15 X2 = 55

XY = 84 N = 5

Step 7: Solve!

420

345

23

23

15

r =

275

23

225

675

529

225

Y = 23 Y2 = 135

X = 15 X2 = 55

XY = 84 N = 5

Step 7: Solve!

75

23

23

15

r =

85.44

146

23

7300

50

225

Y = 23 Y2 = 135

X = 15 X2 = 55

XY = 84 N = 5

Step 7: Solve!

75

23

23

15

.88 =

85.44

146

23

7300

50

225

Y = 23 Y2 = 135

X = 15 X2 = 55

XY = 84 N = 5

Practice

- Page 116 -- # 21

Download Presentation

Connecting to Server..