chapter 7
Download
Skip this Video
Download Presentation
Chapter 7

Loading in 2 Seconds...

play fullscreen
1 / 26

Chapter 7 - PowerPoint PPT Presentation


  • 87 Views
  • Uploaded on

Chapter 7. Correlation, Bivariate Regression, and Multiple Regression. Pearson’s Product Moment Correlation. Correlation measures the association between two variables. Correlation quantifies the extent to which the mean, variation & direction of one variable are related to another variable.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Chapter 7' - nora-tyler


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
chapter 7

Chapter 7

Correlation, Bivariate Regression, and Multiple Regression

pearson s product moment correlation
Pearson’s Product Moment Correlation
  • Correlation measures the association between two variables.
  • Correlation quantifies the extent to which the mean, variation & direction of one variable are related to another variable.
  • r ranges from +1 to -1.
  • Correlation can be used for prediction.
  • Correlation does not indicate the cause of a relationship.
scatter plot
Scatter Plot
  • Scatter plot gives a visual description of the relationship between two variables.
  • The line of best fit is defined as the line that minimized the squared deviations from a data point up to or down to the line.
will a linear fit work1
Will a Linear Fit Work?

y = 0.5246x - 2.2473

R2 = 0.4259

linear fit
Linear Fit

y = 0.0012x - 1.0767

R2 = 0.0035

evaluating the strength of a correlation
Evaluating the Strength of a Correlation
  • For predictions, absolute value of r < .7, may produce unacceptably large errors, especially if the SDs of either or both X & Y are large.
  • As a general rule
    • Absolute value r greater than or equal .9 is good
    • Absolute value r equal to .7 - .8 is moderate
    • Absolute value r equal to .5 - .7 is low
    • Values for r below .5 give R2 = .25, or 25% are poor, and thus not useful for predicting.
significant correlation
Significant Correlation??

If N is large (N=90) then a .205 correlation is significant.

ALWAYS THINK ABOUT R2

How much variance in Y is X accounting for?

r = .205

R2 = .042, thus X is accounting for 4.2% of the variance in Y.

This will lead to poor predictions.

A 95% confidence interval will also show how poor the prediction is.

venn diagram shows r 2 the amount of variance in y that is explained by x
Venn diagram shows (R2) the amount of variance in Y that is explained by X.

R2=.64 (64%) Variance in Y that is explained by X

Unexplained Variance in Y. (1-R2) = .36, 36%

slide13

The vertical distance (up or down) from a data point to the line of best fit is a RESIDUAL.

r = .845

R2 = .714 (71.4%)

Y = mX + b

Y = .72 X + 13

standard error of estimate se e sd of y
Standard Error of Estimate(SEE)SD of Y

Prediction Errors

The SEE is the SD of the prediction errors (residuals) when predicting Y from X. SEE is used to make a confidence interval for the prediction equation.

linear regression statistics
Linear Regression: Statistics

Enter the variables

Click Statistics Button

linear regression output
Linear Regression: Output

71.5% percent of the variance in Y is explained by X.

Correlation (r) r = .845 between X and Y.

regression output
Regression Output

Prediction Equation

Y = .726 (X) + 12.859

95% CI

Y = .726 (X) + 12.859 ± 1.96 (6.06)

example of a 95 confidence interval
Example of a 95% confidence interval.

Both r and SDY are critical in accuracy of prediction.

If SDY is small and r is big, predictions are will be small.

If SDY is big and r is small, predictions are will be large.

We are 95% sure the mean falls between 45.1 and 67.3

multiple regression
Multiple Regression
  • Multiple regression is used to predict one Y (dependent) variable from two or more X (independent) variables.
  • The advantage of multivariate or bivariate regression is
    • Provides lower standard error of estimate
    • Determines which variables contribute to the prediction and which do not.
multiple regression1
Multiple Regression
  • b1, b2, b3, … bn are coefficients that give weight to the independent variables according to their relative contribution to the prediction of Y.
  • X1, X2, X3, … Xn are the predictors (independent variables).
  • C is a constant, similar to Y intercept.
  • Body Fat = Abdominal + Tricep + Thigh
list the variables and order to enter into the equation
List the variables and order to enter into the equation
  • X2 has biggest area (C), it comes in first.
  • X1 comes in next area (A) is bigger than area (E). Both A and E are unique, not common to C.
  • X3 comes in next, it uniquely adds area (E).
  • X4 is not related to Y so it is NOT in the equation.
ideal relationship between predictors and y
Ideal Relationship Between Predictors and Y

Each variable accounts for unique variance in Y

Very little overlap of the predictors

Order to enter?

X1, X3, X4, X2, X5

ad