Objectives Regression analysis is the next step up after correlation; it is used when we want to predict the value of a variable based on the value of another variable. In this case, the variable we are using to predict the other variables value is called the independent variable or sometimes the predictor variable. The variable we are wishing to predict is called the dependent variable or sometimes the outcome variable.
Assumption Variables are approximately normally distributed (see Testing for Normality guide). There is a linear relationship between the two variables. There are classical assumption ……..
Transfer the independent (predictor) variable, hhsize, int Dependent o the Variable "Independent(s):" box and the dependent (outcome) variable, mfx, into the "Dependent:" box. You can do this by either drag-and- Independent Vari dropping or by using the buttons. Click the button.
SPSS will generate quite a few tables in its results section for a linear regression. In this session, we are going to look at the important Model Summary tables Model Summary table. This table provides the R and R2 value. The R value is 0.608, which represents the Adjusted R Std. Error of simple correlation Model R R Square Square the Estimate a and, therefore, indicates a 1 .608 .370 .370 2157.08 high degree of correlation. The R2 value indicates how much of the dependent variable, monthly HH food exp, can be explained by the independent variable, hhsize. In this case, 37.0% can be explained.
The next table is the ANOVA table. This table indicates that ANOVAb the regression model predicts the outcome variable significantly well. How do we know this? Look at the Mean "Regression" row and go Model 1 Regressio Sum of Squares df Square F 3378640742.5 1.0 3378640742 726.116 Sig. .000 a to the Sig. column. n .5 This indicates the statistical significance of the regression model Residual 5746495913.9 123 4653033.1 that was applied. Here, 5.0 P < 0.0005 which is less than 0.05 and indicates that, overall, the model Total 9125136656.4 123 applied is significantly 6.0 good enough in predicting the outcome variable.
The table below, Coefficients, provides us with information on each predictor variable. This provides us with the information necessary to predict monthly food exp from hhsize. We can see that both the constant and hhsize contribute significantly to the model (by looking at the Sig. column). By looking at the B column under the Unstandardized Coefficients column we can present the regression equation as mfx = 669.3+ 861.7(hhsize) Coefficientsa Standardiz ed Coefficient Unstandardized Coefficients s Model B Std. Error Beta t Sig. 1 (Constant) 669.294 151.807 4.409 .000 Household size 861.655 31.976 .608 26.947 .000
Interpretation If HHSIZE goes up by a member or individual, the average monthly HH food expenditure (mfx) goes up by about 862 taka. The intercept value of about 669 taka tells us that if hhsize were zero, mfx would be about 669 taka. The r 2 value of 0.37 means approximately 37 percent of the variation in the mfx is explained by variation in the hhsize. Coefficientsa Standardiz ed Coefficient Unstandardized Coefficients s Model B Std. Error Beta t Sig. 1 (Constant) 669.294 151.807 4.409 .000 Household size 861.655 31.976 .608 26.947 .000