# Estimate Standardized Regression Coefficient Marketing Research Help

Standardization is the process by which the raw data are transformed into new variables that have a mean of 0 and a variance of I. When the data are standardized. the intercept assumes a value of. The term beta coefficient of beta weight is used to denote the standardized regression coefficient. In this case. the slope obtained by the regression of Yon X. Byr is the same as the slope obtained by the regression of X on Y. Bxy Moreover. each of these regression coefficients is equal to the simple correlation between X and Y.

There is a simple relationship between the standardized and non standardized regression coefficients:

For the regression results given in Table 17.2, the value of the beta coefficient is estimated as 0.9361. Note that this is also the value of r calculated earlier in this Once the parameters have been estimated, they can be tested for .signiflcance

Determine the Strength and Significance of Association

A related inference involves determining the strength and significance of the association between Yand X. The strength of association is measured by the coefficient of determination, il. In bivariate regression, il is the square of the simple correlation coefficient obtained by correlating the two variables. The ‘coefficient il varies between 0 and I. It signifies the proportion of the total variation in Ythat is accounted for by the variation in X. The decomposition of the total variation in Yis similar to that for analysis of variance .As shown in Figure 17.6, the total variation, SSy’ may be decomposed into the variation accounted for by the regression line, SSrrg’ and the error or residual variation, SS<rroror SSrrJ’ as follows

where

The strength of association may then be calculated as follows:

To illustrate the calculations of let us consider again the regression of attitude toward the city on the duration of residence. It may be recalled from earlier calculations of the simple correlation coefficient that:

The predicted values (f) can be calculated using the regression equation:

Attitude (f) = I JJ793 + 0.5897 (Duration of residence)

For the first observation in Table 17.1, this value is:

(Y) = 1.0793 + 0.5897 X 10 = 6.9763

For each successive observation, the predicted values are, in order, 8.1557,8.1557,3.4381, 8.1557,4.6175,5.7969,2.2587,11.6939,6.3866,11.1042, and 2.2587. Therefore

Multiple Regression

Multiple regression involves a single dependent variable and two or more independent variables. The questions raised in the context of bivariate regression can also be answered via multiple regression by considering additional independent variables

Can variation in sales be explained in terms of variation in advertising expenditures, prices, and level of distribution?

• Can variation in market shares be accounted for by the size of the sales force, advertising expenditures, and sales promotion budgets?
• Are consumers’ perceptions of quality determined by their perceptions of prices, brand image, and brand attributes?

• How much of the variation in sales can be explained by advertising expenditures, prices, and level of distribution?
• What is the contribution of advertising expenditures in explaining the variation in sales when the levels of prices and distribution are controlled?
• What levels of sales may be expected, given the levels of advertising expenditures, prices, and level of distribution?