Anova Table
Sourcea | SSb dfc MSd -------------+------------------------------
Model | 9543.72074 4 2385.93019
Residual | 9963.77926 195 51.0963039 -------------+------------------------------
大班安全教育教案20篇
Total | 19507.5 199 98.0276382
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买卖房屋正规合同a. Source - This is the source of variance, Model, Residual, and Total. The Total variance is partitioned into the variance which can be explained by the independent variables (Model) and the variance which is not explained by the independent variables (Residual, sometimes called Error). Note that the Sums of Squares for the Model and Residual add up to the Total Variance, reflecting the fact that the Total Variance is partitioned into Model and Residual variance. 好看的福字
b. SS - The are the Sum of Squares associated with the three sources of variance, Total,
Model and Residual. The can be computed in many ways. Conceptually, the formulas can be expresd as:
SSTotal The total variability around the mean. S(Y - Ybar)2.
煎牛排怎么煎 SSResidual The sum of squared errors in prediction. S(Y - Ypredicted)2.
SSModel The improvement in prediction by using the predicted value of Y over just using the mean of Y. Hence, this would be the squared differences between the predicted value of Y and the mean of Y, S(Ypredicted - Ybar)2. Another way to think of this is the SSModel is SSTotal - SSResidual. Note that the SSTotal = SSModel + SSResidual. Note that SSModel / SSTotal is equal to .4892, the value of R-Square. This is becau R-Square is the proportion of the variance explained by the independent variables, hence can be computed by SSModel / SSTotal.
c. df - The are the degrees of freedom associated with the sources of variance. The total variance has N-1 degrees of freedom. In this ca, there were N=200 students, so t
he DF for total is 199. The model degrees of freedom corresponds to the number of predictors minus 1 (K-1). You may think this would be 4-1 (since there were 4 independent variables in the model, math, female, socst and read). But, the intercept is automatically included in the model (unless you explicitly omit the intercept). Including the intercept, there are 5 predictors, so the model has 5-1=4 degrees of freedom. The Residual degrees of freedom is the DF total minus the DF model, 199 - 4 is 195.
d. MS - The are the Mean Squares, the Sum of Squares divided by their respective DF. For the Model, 9543.72074 / 4 = 2385.93019. For the Residual, 9963.77926 / 195 = 51.0963039. The are computed so you can compute the F ratio, dividing the Mean Square Model by the Mean Square Residual to test the significance of the predictors in the model.
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Overall Model Fit
Number of ob = 200 F( 4, 195)f = 46.69 Prob > Ff = 0.0000 R-squaredg = 0.4892 Adj R-squaredh = 0.4788 Root MSEi = 7.1482
e. Number of obs - This is the number of obrvations ud in the regression analysis.
f. F and Prob > F - The F-value is the Mean Square Model (2385.93019) divided by the Mean Square Residual (51.0963039), yielding F=46.69. The p-value associated with this F value is very small (0.0000). The values are ud to answer the question "Do the independent variables reliably predict the dependent variable?". The p-value is compared to your alpha level (typically 0.05) and, if smaller, you can conclude "Yes, the independent variables reliably predict the dependent variable". You could say that the group of variables math and female can be ud to reliably predict science (the dependent variable). If the p-value were greater than 0.05, you would say that the group of independent variables does not show a statistically significant relationship with the dependent variable, or that the group of independent variables does not reliably predict the dependent variable. Note that this is an overall significance test asssing whether th
e group of independent variables when ud together reliably predict the dependent variable, and does not address the ability of any of the particular independent variables to predict the dependent variable. The ability of each individual independent variable to predict the dependent variable is addresd in the table below where each of the individual variables are listed.
g. R-squared - R-Squared is the proportion of variance in the dependent variable (science) which can be predicted from the independent variables (math, female, socst and read). This value indicates that 48.92% of the variance in science scores can be predicted from the variables math, female, socst and read. Note that this is an overall measure of the strength of association, and does not reflect the extent to which any particular independent variable is associated with the dependent variable.
h. Adj R-squared - Adjusted R-square. As predictors are added to the model, each predictor will explain some of the variance in the dependent variable simply due to chance. One could continue to add predictors to the model which would continue to impr
ove the ability of the predictors to explain the dependent variable, although some of this increa in R-square would be simply due to chance variation in that particular sample. The adjusted R-square attempts to yield a more honest value to estimate the R-squared for the population. The value of R-square was .4892, while the value of Adjusted R-square was .4788 Adjusted R-squared is computed using the formula 1 - ((1 - Rsq)((N - 1) /( N - k - 1)). From this formula, you can e that when the number of obrvations is small and the number of predictors is large, there will be a much greater difference between R-square and adjusted R-square (becau the ratio of (N - 1) / (N - k - 1) will be much greater than 1). By contrast, when the number of obrvations is very large compared to the number of predictors, the value of R-square and adjusted R-square will be much clor becau the ratio of (N - 1)/(N - k - 1) will approach 1.
戒指戴食指i. Root MSE - Root MSE is the standard deviation of the error term, and is the square root of the Mean Square Residual (or Error).御台所
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Parameter Estimates
------------------------------------------------------------------------------ sciencej | Coef.k Std. Err.l tm P>|t|m [95% Conf. Interval]n -------------+---------------------------------------------------------------- math | .3893102 .0741243 5.25 0.000 .243122 .5354983 female | -2.009765 1.022717 -1.97 0.051 -4.026772 .0072428 socst | .0498443 .062232 0.80 0.424 -.0728899 .1725784 read | .3352998 .0727788 4.61 0.000 .1917651 .4788345 _cons | 12.32529 3.193557 3.86 0.000 6.026943 18.62364 ------------------------------------------------------------------------------
