Predicted Values The observed, unadjusted means for achievement, IQ, and motivation are presented in Table 3 below. (1) What is the literal interpretation for b0 = 32.365? (2) What is the literal interpretation for b1 = 6.171(Smith)? (3) What is the literal interpretation for b2 =12.023(Collins)? (4) What is the literal interpretation for b3 = 0.415(IQ)? (5) What is the literal interpretation for b4 =0.177(MOTIVATION)? 2. One minor difference is that dummy variables now represented the adjusted mean difference between groups, adjusted for the statistical effects of the quantitative predictors (the covariates). Interpretation of coefficients remains the same as with previous multiple regression models discussed. These are control variables used to adjust or equate groups, or to partial effects of confounding variables. Since this above equation contains both qualitative and quantitative predictors, this model is identical to an Analysis of Covariance (ANCOVA) where the two quantitative predictors, IQ and Motivation, are known as EDUR 8132 4:03:03 PM 1Ĭovariates. This is the same logic discussed earlier with multiple regressions. Since regression equation contains multiple predictors, the represent partial statistical effects-the statistical association between X1 and Y controlling for X2. Table 2: SPSS results for data in Table 1 Unstandardized Coefficientsĩ5% Confidence Interval for B Lower Upper Bound Bound 7.862 56.867 The SPSS estimates are provided below in Table 2. Where Smiht (1 = in Smith’s class, 0 = other) and Collins (1 = in Collin’s class, 0 = other) are dummy variables. The regression would be: Yi = b0 + b1Smith1i + b2Collins2i + b3IQ3i + b4MOTIVATION4i + ei, Regression Equation With both qualitative and quantitative predictors, the regression equation remains unchanged except with the addition of coefficients to capture the statistical effect of the predictors. Multiple Linear Regression with Qualitative and Quantitative Independent Variables 1.