Question

Models 1-7 are below

$Regression [DataSetll C:\Usersn.little5773 Downloads\child data.sav Variables Entered/Removed Variables Entered Variables Rem$

Part C: Select one model you would use to explain reading ability.,Then use that model to find the 95% confidence interval estimate for the mean reading ability 95% prediction interval for reading ability When age 6, mem span 4.2 and ig 91. Regression [DataSetll C:\Usersn.little5773 Downloads\child data.sav Variables Entered/Removed Variables Entered Variables Removed Method Model Enter age a. Dependent Variable: reading ability b. All requested variables entered. Model Summary Adjusted R Square Std. Error o R Square 716 a. Predictors: (Constant, age the Estimate Model 846a 700 37661 ANOVAa Sum of Squares Mean Square df Sig Model 6.427 2.553 8.980 000b Regression Residual Total 6.427 45.313 142 18 19 a. DependentVariable: reading ability b. Predictors: (Constant), age Coefficients Standardized Unstandardized Coefficients Coefficients Std. Error Beta Sig Model 493 6.155 (Constant) 3.032 081 542 846 6.731 age a. DependentVariable: reading ability Regression Variables Entered/Removed Variables Removed Variables Entered Method Model short-term Enter memory span a. Dependent Variable: reading ability b. All requested variables entered. Model Summary Adjusted R Square Std . Error of he Estimate R Square Model 673 821 655 40374 a. Predictors: (Constant), short-term memory span ANOVA Sum of Squares df Mean Square 6.046 163 Sig Model 000b Regression Residual Total 6.046 2.934 8.980 37.091 19 a. Dependent Variable: reading ability b. Predictors: (Constant), short-term memory span Coefficients Standardized Unstandardized Coefficients Coefficients Beta Std. Error Sig Model 731 160 (Constant) short-term memory span 1.880 2.571 019 6.090 821 a. Dependent Variable: reading ability Regression Variables Entered/Removed Variables Entered Variables Removed Method Model Enter IQ a. Dependent Variable: reading ability b. All requested variables entered. Model Summary Adjusted R Square Std. Error of the Estimate R Square 023 a. Predictors: (Constant), IQ Model 69829 150 .032 ANOVAa Sum of Squares df Mean Square 203 488 Sig Model -203 527b Regression Residual Total 417 18 8.980 19 a. Dependent Variable: reading ability b. Predictors: (Constant), IQ Coefficients Standardized Coefficients Beta Unstandardized Coefficients Std. Error Sig Model 4.719 2.454 025 070 527 Constant) IQ 1.923 016 150 645 a. Dependent Variable: reading ability Regression Variables Entered/Removed Variables Removed Variables Entered shor-term memory span, age Method Model Enter a. Dependent Variable: reading ability b. All requested variables entered. Model Summary Adjusted FR Square Std. Error of the Estimate 31920 R Square Model 784 807 898a a. Predictors: (Constant), short-term memory span, age ANOVA Sum of Squares df Mean Square Sig Model 000b Regression Residual Total 7.248 1.732 8.980 3.624 35.568 17 102 a. Dependent Variable: reading ability b. Predictors: (Constant), short-term memory span, age Coefficients" Standardized Coefficients Beta Unstandardized Coefficients 8 Std. Error Sig Model 1.897 339 521 3.281 3.435 2.839 (Constant age short-term memory span 578 099 184 004 003 011 530 438 a. Dependent Variable: reading ability Regression Variables Entered/Removed Variables Entered Variables Removed Model Method IQ, ageb Enter a. Dependent Variable: reading ability b. All requested variables entered Model Summary Adjusted R Square Std. Error of the Estimate R Square Model 821 800 906a 30739 a. Predictors: (Constant), IQ, age ANOVAa Sum of Squares Sig df Mean Square Model 3.687 39.018 000b 7.374 1.606 8.980 Regression Residual Total 17 094 19 a. Dependent Variable: reading ability b. Predictors: (Constant), IQ, age Coefficients Standardized Unstandardized Coefficients Coefficients Std. Error Beta Sig Model 580 (Constant) age IO .703 584 036 1.247 067 011 .564 912 3.165 006 331 a. Dependent Variable: reading ability Regression Variables Entered/Removed Variables Entered IQ, short-term memory span Variables Removed Method Model Enter a. Dependent Variable: reading ability b. All requested variables entered. Model Summary Adjusted R Square Std. Error of the Estimate R Square Model 827 684 647 40870 a. Predictors: (Constant), IQ, short-term memory span ANOVA Sum of Squares df Mean Square Sig. Model 3.070 18.381 ,000b Regression Residual Total 6.140 2.840 8.980 167 19 a. Depenent Variable: reading ability b. Predictors: (Constant), IQ, short-term memory span Coefficients Unstandardized Coefficients Coefficients Std. Error Beta Sig Model 1.929 5.962 752 071 Constant) short-term memory span IQ 2.836 1.015 012 1.471 170 016 853 462 108 a. Dependent Vaiable: reading ability Regression Variables Entered/Removed Variables Entered Q, age, short- term memory Variables Removed Method Model Enter a. Dependent Variable: reading ability b. All requested variables entered. Model Summary Adjusted R Square Std. Error of the Estimate R Square Model 804 914 30435 835 a. Predictors: (Constant), IQ, age, short-term memory span ANOVA Sum of Squares Sig. df Mean Square Model 2499 26 982 .000 Regression Residual Total 7.498 1.482 8.980 093 19 a. Dependent Variable: reading ability b. Predictors: (Constant), Q, age, short-term memory span Coefficients Standardized Unstandardized Coefficients Coefficients Std. Error Beta Sig. Model 106 466 269 025 1.338 122 -233 015 (Constant) age short-term memory span IQ 079 3.828 1.158 1.643 938 001 264 120 727 226 226 a. Dependent Variable: reading ability

Answer 1

we use the model with age, short-term memory span and IQ as independent variables

y^ = -0.106 + 0.466 age + 0.269 memory span + 0.025 IQ

se = 0.30435
df = 16

point estimate =
y^ = -0.106 + 0.466 age + 0.269 memory span + 0.025 IQ
= -0.106 + 0.466 *6 + 0.269 *4.2 + 0.025*91
= 6.0948

t = t.inv.2t(0.05,16) = 2.1199

95% approx confidence interval
= y^ +- t * 0.4*se
=6.0948 +- 2.12 * 0.4*0.30435
= ( 5.8367 , 6.35288 )
95% approximate prediction interval
= y^ +- t * 1.1*se
= 6.0948 +- 2.12 * 1.1*0.30435
= ( 5.38505 , 6.80454)