The residual sum of squaresĪssuming a desired significance level of 0.05, the hypothesis of no temperature effect is clearly rejected. In this case, the so-called total coefficient for the simple linear regression model includes the indirect effect of other variables, while in the multiple regression model, the coefficient measures only the effect of TEMP by holding constant the effects of other variables.įor the second step we compute the partitioning of the sums of squares. Note that the coefficient for TEMP is 0.9130 in the multiple regression model, while it was 1.681 for the simple linear regression involving only the TEMP variable. Because of the different scales of the independent variables, the relative magnitudes of these coefficients have little meaning and also are not indicators of relative statistical significance. The remainder of the coefficients are positive, indicating later departure times for increased values of TEMP, HUM, LIGHT, and CLOUD. Unlike the case of the regression involving only TEMP, the intercept now has no real meaning since zero values for HUM and LIGHT cannot exist. The five elements in the last column, labeled TIME, of the inverse portion contain the estimated coefficients, providing the equation: X′X Inverse, Parameter Estimates, and SSE Therefore all calculations in this example will be based on the remaining 36 observations. Fortunately, most computer programs recognize missing values and will automatically ignore such observations. This means that these observations cannot be used for the regression analysis.
1 6 3 2.Īs expected, the confidence intervals of those coefficients deemed statistically significant at the 0.05 level do not include zero.Īge: Std.
We can use this output to compute the confidence intervals for the coefficients in the regression equation as follows:Īge: Std. A typical computer output for Example 8.2 is shown in Table 8.6. For these reasons, most computers provide the standard errors and t tests. In Chapter 7 we noted that the use of the t statistic allowed us to test for specific (nonzero) values of the parameters, and allowed the use of one- tailed tests and the calculation of confidence intervals.