Linear Regression - Topics

1 / 17

# Linear Regression - Topics - PowerPoint PPT Presentation

Linear Regression - Topics. Basics of Linear Regression Variation in Linear Regression Linear Regression Analysis Goodness of Fit Standard Error terms for Linear Regression Hypothesis testing. Regression - Types. Linear Regression.

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

## PowerPoint Slideshow about 'Linear Regression - Topics' - ellema

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

Linear Regression - Topics

• Basics of Linear Regression
• Variation in Linear Regression
• Linear Regression Analysis
• Goodness of Fit
• Standard Error terms for Linear Regression
• Hypothesis testing

Linear Regression

• A statistical technique that uses a single, independent variable (X) to estimate a single dependent variable (Y).
• Based on the equation for a line:

Y = b + mX

e

=

b b

+

Y

X

i

0 1

Linear Regression - Model

Y

? (the actual value of Yi)

Yi

X

Xi

Linear Regression - Model

Population

Regression Coefficients for a . . .

ˆ

Sample

Y = b0 + b1Xi + e

ˆ

Y = b0 + b1Xi

ANOVA CRD - Variation

SST is a measure of the total variation of observations. A measure of the differences in observations.

SSTR

Due to treatments.

SST

SSE

SST = SSTR + SSE

Random/unexplained.

Linear Regression - Variation

Ice Cream Example

Y

Y

= 2.53

Linear Regression - Variation

Ice Cream Example

Sample Regression Line

Regression Model

Linear Regression - Variation

SSR

Due to regression.

SST

SSE

SST = SSR + SSE

Random/unexplained.

Linear Regression - Variation

Y

SSE =(Yi-Yi )2

_

SST =(Yi-Y)2

_

SSR = (Yi -Y)2

_

Y

X

Xi

Determining the Regression Line/Model

• Use Excel (or any other popular statistical software)
• Select Tools, Data Analysis, Regression
• Provide the X range
• Provide the Y range
• Output the analysis to a new sheet
• Manual Calculations

_

SSy =(Yi - Y)2

_

_

SSxy =(Xi - X)(Xi - Y)

SSE

=

S

YX

n-2

Determining the Regression Line/Model Manual Calculations

_

_

SSE =(Yi-Yi )2

SSR = (Yi -Y)2

SST =(Yi-Y)2

_

b1=SSxy/SSx

SSx =(Xi - X)2

_

_

b0 = Y – b1X

MSE = SSE / df

MSR = SSR / df

R2 = SSR/SST

t-test = b1 / Sb1

Measures of Model Goodness
• R2 – Coefficient of Determination
• F-test > F-crit or p-value less than alpha
• Standard Error
• t-test
Hypothesis testing for
• Testing to see if the linear relationship between X and Y is significant at the population level.
• t-test
• H0:

HA:

• t-crit, alpha or alpha/2, n-2 df
Standard Error Terms in Linear Regression
• Se(standard error of the estimate)

A measure of variation around the regression line

If the Se is small…

Standard deviation Of the Errors

• Sb1(standard error of the the sampling distribution of b1)

Standard deviation of the slopes

A measure of the variation of the slopes from different samples If the Sb1 is small…our b1 estimate is probably very accurate

Estimates of …

b1

b1

b1

Linear Regression Example
• Petfood, Estimate Sales based on Shelf Space
• Two sets of samples, 12 observations each
• Perform a Regression Analysis on both sets of data

Sample1

Sample2