Used to investigate and model the relationship between a response variable and one or more predictors.
You can use Multiple Linear Regression to perform simple and multiple regression using least squares. Use this procedure for fitting general least squares models, storing regression statistics and generating prediction and confidence intervals.
Select the column containing the Y, or response variable.
Select the columns containing the X, or predictor variables.
The display of outputs of VisualStat.
Enter response and predictor variables in numeric columns of equal length so that each row in your worksheet contains measurements on one observation or subject. VisualStat excludes all observation that contains missing values in the response or in the predictors.
Check to display an analysis of variance table
Check to display regression coefficients, including value, standard error, beta, t value, p value and confidence interval.
Check to store the residuals.
Check to store the value the model predicts for the dependent variable.
Check to store the (X'X)-1 matrix.
Check to store the variance-covariance matrix.
Check to store the leverage values.
Check to store Cook's distance.
Check to store the DFITS.
Displays a histogram, and a scatter plot.
•Histogram of residuals:
Check to display a histogram of the residuals.
•Residuals vs fits:
Check to plot the residuals versus the fitted values.
•Include constant in equation:
Check to fit a constant term (the y-intercept of the regression line). Uncheck to fit the model without a constant term. VisualStat does not display R2 for this model.
Enter the test mean µ0
•Confidence Level: Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.
Using the Consumer Price Index dataset we can explore the relationship between the prices of various products and commodities. These data represent the average prices of the following items for the months of January between 1981 and 2006.
1.Open the DataBook reg.vstz
2.Select the sheet ConsumerPriceIndex
3.Choose the tab Statistics, the group Regression and the command Regression
4.In Response, select Gasoline. In Predictors, select Electricity, Fuel_Oil and Orange_Juice.
Report window output
Multiple Linear Regression
The regression equation is
Gasoline = 0.0829 + 0.0132*Electricity + 0.7934*Fuel_Oil - 0.1903*Orange_Juice
Min 1Q Median 3Q Max
-0.1973 -0.0357 0.0122 0.0388 0.0875
Value Std. Error Beta t value p value 95% LBound 95% UBound
(Intercept) 0.0829 0.1250 0.0000 0.6635 0.5139 0.0750 0.0908
Electricity 0.0132 0.0034 0.2375 3.9359 0.0007 0.0130 0.0134
Fuel_Oil 0.7934 0.0445 0.8890 17.8195 0.0000 0.7905 0.7962
Orange_Juice -0.1903 0.0867 -0.1228 -2.1953 0.0390 -0.1958 -0.1848
Multiple R-Squared 0.9581
Adjusted R-Squared 0.9524
Residual Std Error 0.0676
Analysis of Variance
df Sum of Sq Mean Sq F Value Pr(F)
Regression 3 2.3007 0.7669 167.8123 0.0000
Residual 22 0.1005 0.0046
Total 25 2.4012
Regressing Gasoline on the following three predictor prices: Orange Juice, Fuel and Electricity illustrates significant effects of all these variables as significant explanatory prices (at a = 0.05) for the cost of Gasoline between 1981 and 2006.
Web Resource: Probability and statistics EBook