excel multiple regression n.
Download
Skip this Video
Download Presentation
EXCEL: Multiple Regression

Loading in 2 Seconds...

play fullscreen
1 / 10

EXCEL: Multiple Regression - PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on

EXCEL: Multiple Regression. Regression Model. A multiple regression model is: y = β 1 + β 2 x 2 + β 3  x 3 + u Such that: y is dependent variable x 2 and x 3 are independent variables β 1 is constant β 2 and β 3 are regression coefficients

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 'EXCEL: Multiple Regression' - tarik-beck


Download Now 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
regression model
Regression Model
  • A multiple regression model is:

y = β1+ β2 x2+ β3 x3+ u

Such that:

    • y is dependent variable
    • x2and x3are independent variables
    • β1 is constant
    • β2and β3are regression coefficients
    • It is assumed that the error u is independent with constant variance.
  • We wish to estimate the regression line:

y = b1 + b2 x2 + b3 x3

regression analysis in excel
Regression Analysis in Excel
  • We do this using the Data analysis Add-in and Regression.
  • Example:
regression analysis in excel2
Regression Analysis in Excel
  • The regression output has three components:
    • Regression statistics table
    • ANOVA table
    • Regression coefficients table.
interpreting regression statistics table regression statistics
Interpreting Regression Statistics TableRegression Statistics
  • The standard error here refers to the estimated standard deviation of the error term u.
  • It is sometimes called the standard error of the regression. It equals sqrt(SSE/(n-k)).
  • It is not to be confused with the standard error of y itself (from descriptive statistics) or with the standard errors of the regression coefficients given below.
  • R2 = 0.8025 means that 80.25% of the variation of yi around its mean is explained by the regressors x2i and x3i.
interpreting regression statistics table regression coefficients table
Interpreting Regression Statistics TableRegression coefficients table
  • The regression output of most interest is the following table of coefficients and associated output:
interpreting regression statistics table regression coefficients table1
Interpreting Regression Statistics TableRegression coefficients table
  • Let βjdenote the population coefficient of the jth regressor (intercept, HH SIZE and CUBED HH SIZE). Then
    • Column "Coefficient" gives the least squares estimates of βj.
    • Column "Standard error" gives the standard errors (i.e.the estimated standard deviation) of the least squares estimates bj of βj.
    • Column "t Stat" gives the computed t-statistic for H0: βj = 0 against Ha: βj ≠ 0.This is the coefficient divided by the standard error. It is compared to a t with (n-k) degrees of freedom where here n = 5 and k = 3.
    • Column "P-value" gives the p-value for test of H0: βj = 0 against Ha: βj ≠ 0..This equals the Pr{|t| > t-Stat}where t is a t-distributed random variable with n-k degrees of freedom and t-Stat is the computed value of the t-statistic given in the previous column. Note that this p-value is for a two-sided test. For a one-sided test divide this p-value by 2 (also checking the sign of the t-Stat).
    • Columns "Lower 95%”and "Upper 95%”values define a 95% confidence interval for βj.
interpreting regression statistics table regression coefficients table2
Interpreting Regression Statistics TableRegression coefficients table
  • A simple summary of the previous output is that the fitted line is:

y = 0.8966 + 0.3365x + 0.0021z

ad