1 / 10

# EXCEL: Multiple Regression - PowerPoint PPT Presentation

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

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

## PowerPoint Slideshow about ' EXCEL: Multiple Regression' - tarik-beck

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

### EXCEL: Multiple Regression

• 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

• We do this using the Data analysis Add-in and Regression.

• Example:

• The regression output has three components:

• Regression statistics table

• ANOVA table

• Regression coefficients table.

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 TableRegression coefficients table

• The regression output of most interest is the following table of coefficients and associated output:

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 TableRegression coefficients table

• A simple summary of the previous output is that the fitted line is:

y = 0.8966 + 0.3365x + 0.0021z