Mean Square Error Spss Regression
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page shows an example regression analysis with footnotes explaining the output. These data (hsb2) were collected on 200 high schools students and are scores on various tests, including science, math, reading and social studies (socst). The variable female is a dichotomous variable coded 1 interpreting multiple regression output spss if the student was female and 0 if male. In the syntax below, the get file
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command is used to load the data into SPSS. In quotes, you need to specify where the data file is located on your computer. In how to report regression results spss the regression command, the statistics subcommand must come before the dependent subcommand. You list the independent variables after the equals sign on the method subcommand. The statistics subcommand is not needed to run the regression, but on it we can spss output interpretation specify options that we would like to have included in the output. Please note that SPSS sometimes includes footnotes as part of the output. We have left those intact and have started ours with the next letter of the alphabet. get file "c:\hsb2.sav". regression /statistics coeff outs r anova ci /dependent science /method = enter math female socst read. Variables in the model c. Model - SPSS allows you to specify multiple models in a single regression command. This tells you
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the number of the model being reported. d. Variables Entered - SPSS allows you to enter variables into a regression in blocks, and it allows stepwise regression. Hence, you need to know which variables were entered into the current regression. If you did not block your independent variables or use stepwise regression, this column should list all of the independent variables that you specified. e. Variables Removed - This column listed the variables that were removed from the current regression. Usually, this column will be empty unless you did a stepwise regression. f. Method - This column tells you the method that SPSS used to run the regression. "Enter" means that each independent variable was entered in usual fashion. If you did a stepwise regression, the entry in this column would tell you that. Overall Model Fit b. Model - SPSS allows you to specify multiple models in a single regression command. This tells you the number of the model being reported. c. R - R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. d. R-Square - This is the proportion of variance in the dependent variable (science) which can be explained by the independent variables (math, female, socst and read). 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. e. A
Annotated SPSS Output for Simple Regression Analysis This page shows an example simple regression analysis with footnotes explaining the output. The analysis uses a data file about scores obtained by elementary schools, predicting api00 standardized coefficients beta interpretation spss from enroll using the following SPSS commands. regression /dependent api00 /method=enter enroll. The output of linear regression analysis spss this command is shown below, followed by explanations of the output. Variables Entered/Removed(b)a Model Variables Entered Variables Removed Method 1 ENROLL(a)
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. Enter a All requested variables entered.b Dependent Variable: API00 Model Summary Model Rb R Squarec Adjusted R Squared Std. Error of the Estimatee 1 .318(a) .101 .099 135.026 a Predictors: (Constant), ENROLL ANOVA(b) Modelf Sum http://www.ats.ucla.edu/stat/spss/output/reg_spss.htm of Squaresg dfh Mean Squarei Fj Sig.j 1 Regression 817326.293 1 817326.293 44.829 .000(a) Residual 7256345.704 398 18232.024 Total 8073671.997 399 a Predictors: (Constant), ENROLLb Dependent Variable: API00 Coefficients(a) Unstandardized Coefficients Standardized Coefficients to Sig.o Modelk Bl Std. Errorm Betan 1 (Constant) 744.251 15.933 46.711 .000 ENROLL -.200 .030 -.318 -6.695 .000 a Dependent Variable: API00 Footnotes a. This is a summary of the analysis, showing that api00 was the dependent http://www.ats.ucla.edu/stat/spss/webbooks/reg/chapter1/annotated1.htm variable and enroll was the predictor variable. b. R is the square root of R Square (shown in the next column). c. R Square is the proportion of variance in the dependent variable (api00) which can be predicted from the independent variable (enroll). This value indicates that 10% of the variance in api00 can be predicted from the variable enroll. d. 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 improve the ability of the predictors to explain the dependent variable, although some of this increase 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 .10, while the value of Adjusted R-square was .099. Adjusted R-squared is computed using the formula 1 - ( (1-R-sq)(N-1 / N - k - 1) ). From this formula, you can see that when the number of observations is small and the number of predictors is large, there will be a much greater difference between R-square and adjusted R-square (because the ratio of (N-
Annotated SPSS Output for Multiple Regression Analysis This page shows an example multiple regression analysis with footnotes explaining the output. The analysis uses a data file about scores obtained by elementary http://www.ats.ucla.edu/stat/spss/webbooks/reg/chapter1/annotated2.htm schools, predicting api00 from ell, meals, yr_rnd, mobility, acs_k3, acs_46, full, emer and enroll http://www.jerrydallal.com/lhsp/regout.htm using the following SPSS commands. This example uses the elemapi2 dataset. regression /dependent api00 /method=enter ell meals yr_rnd mobility acs_k3 acs_46 full emer enroll. Variables Entered/Removed(b)a Model Variables Entered Variables Removed Method 1 ENROLL, ACS_46, MOBILITY, ACS_K3, EMER, ELL, YR_RND, MEALS, FULL(a) . Enter a All requested variables entered.b Dependent Variable: API00 Model Summary Modelb Rc multiple regression R Squared Adjusted R Squaree Std. Error of the Estimatef 1 .919(a) .845 .841 56.768 a Predictors: (Constant), ENROLL, ACS_46, MOBILITY, ACS_K3, EMER, ELL, YR_RND, MEALS, FULL ANOVA(b) Modelg Sum of Squaresh dfi Mean Squarej Fk Sig.k 1 Regression 6740702.006 9 748966.890 232.409 .000(a) Residual 1240707.781 385 3222.618 Total 7981409.787 394 a Predictors: (Constant), ENROLL, ACS_46, MOBILITY, ACS_K3, EMER, ELL, YR_RND, MEALS, FULLb Dependent Variable: API00 Coefficients(a) Unstandardized Coefficients regression analysis spss Standardized Coefficients tp Sig.p Modell Bm Std. Errorn Betao 1 (Constant) 758.942 62.286 12.185 .000 ELL -.860 .211 -.150 -4.083 .000 MEALS -2.948 .170 -.661 -17.307 .000 YR_RND -19.889 9.258 -.059 -2.148 .032 MOBILITY -1.301 .436 -.069 -2.983 .003 ACS_K3 1.319 2.253 .013 .585 .559 ACS_46 2.032 .798 .055 2.546 .011 FULL .610 .476 .064 1.281 .201 EMER -.707 .605 -.058 -1.167 .244 ENROLL -1.216E-02 .017 -.019 -.724 .469 a Dependent Variable: API00 a. This is a summary of the regression analysis performed. It lists the predictor variables and the outcome variable. It indicates that there was only one model tested and that all of the predictor variables were entered for that model. b. This is a list of the models that were tested. In this case, there was only one model used. c. R is the square root of R Square (shown in the next column). d. R-Square is the proportion of variance in the dependent variable (api00) which can be predicted from the independent variables (ell, meals, yr_rnd, mobility, acs_k3, acs_46, full, emer and enroll). This value indicates that 84% of the variance in api00 can be predicted from the variables ell, meals, yr_rnd, mobility, acs_k3, acs_46, full, emer and enroll. Note that this i
is, vitamin B12 and CLC are being used to predict homocysteine. A (common) logarithmic transformation had been applied to all variables prior to formal analysis, hence the initial L in each variable name, but that detail is of no concern here. Dependent Variable: LHCY Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 2 0.47066 0.23533 8.205 0.0004 Error 233 6.68271 0.02868 C Total 235 7.15337 Root MSE 0.16936 R-square 0.0658 Dep Mean 1.14711 Adj R-sq 0.0578 C.V. 14.76360 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 1.570602 0.15467199 10.154 0.0001 LCLC 1 -0.082103 0.03381570 -2.428 0.0159 LB12 1 -0.136784 0.06442935 -2.123 0.0348 Parameter Estimates. The column labeled Variable should be self-explanatory. It contains the names of the predictor variables which label each row of output. DF stands for degrees of freedom. For the moment, all entries will be 1. Degrees of freedom will be discussed in detail later. The Parameter Estimates are the regression coefficients. The regression equation is LHCY = 1.570602 - 0.082103 LCLC - 0.136784 LB12 To find the predicted homocysteine level of someone with a CLC of 12.3 and B12 of 300, we begin by taking logarithms. Log(12.3)=1.0899 and log(300)=2.4771. We then calculate LHCY = 1.570602 - 0.082103 1.0899 - 0.136784 2.4771 = 1.1423 Homocysteine is the anti-logarithm of this value, that is, 101.1423 = 13.88. The Standard Errors are the standard errors of the regression coefficients. They can be used for hypothesis testing and constructing confidence intervals. For example, confidence intervals for LCLC are constructed as (-0.082103 k 0.03381570), where k is the appropriate constant depending on the level of confidence desired. For example, for 95% confidence intervals based on large samples, k would be 1.96. The T statistic tests the hypothesis that a population regression coefficient is 0 WHEN THE OTHER PREDICTORS ARE IN THE MODEL. It is the ratio of the sample regression coefficient to its standard error. The statistic has the form (estimate - hypothesized value) / SE. Since the hypothesized value is 0, the stat