Directions: For this assignment you will need to download the SPSS dataset \"Data File.sav\". In order to receive full credit, you must turn in all SPSS output and hand calculations associated with your answers. However, please do not assume that just including SPSS output is the same as answering the questions. Be sure to read and answer all the questions and clearly label on your output(s) where you have found your answers. For this homework assignment you are asked to evaluate the relationship between attitude towards math and performance on a standardized mathematics assessment for high school freshman and high school seniors. \"Freshmen\" will serve as the reference group for the dummy coded age variable. A high score on the attitudes toward mathematics scale reflects the student has a more positive attitude towards mathematics. Scores on this measure can range from 0 to 12. Higher scores on the standardized mathematics assessment indicate higher performance with a possible score range of 0 to 100. Hint: A key to understanding this homework is to remember how the coding of 0s and 1s work in dummy coding for both the main effects, the adjusted main effects as well as the interaction effect. 1. a. Do the slopes in the regression model predicting math performance from the attitudes toward math scale differ for high school freshmen and seniors? What evidence do you have to j ustify your decision? This includes providing the parameter(s) being estimated, the statistical test(s) (F, t, etc.) and its (their) value, degrees of freedom and the obtained significance level(s). b. If the slopes are found to differ, what are the two separate regression lines that predict math performance from the attitudes toward math scale for high school freshmen and seniors? Justify your answer using information from your output. Please answer this question regardless of your decision for question 1a. c. In a model in which the slopes for the regression model predicting math performance from the attitudes toward math scale do/would differ, how would you evaluate whether the Y-intercepts from this model are different across the age groups? What evidence would you use to demonstrate this? This includes providing the parameter(s) being estimated, the statistical test(s) (F, t, etc.) and its (their) value, degrees of freedom and the obtained significance level(s). 2. If the slopes in the regression model predicting math performance from the attitudes toward math scale do not differ significantly for high school freshmen and seniors, what would be the \"common\" slope to be used in the prediction equation? How do you find the common slope? Provide the steps, evidence, and information you are using for your decision. Please answer this question regardless of your decision for question 1a. 3. a. Do the Y-intercepts when using a common slope differ for high school freshmen and seniors? Provide evidence for justifying your answer. This includes providing the parameter(s) being estimated, the statistical test(s) (F, t, etc.) and its (their) value, degrees of freedom and the obtained significance level(s). b. What are the values of the Y-intercepts for high school freshmen and seniors when using a common slope? c. Using the values based on your decisions in questions 3a and 3b, and the \"common\" slope, what are the regression equations that should be used separately for high school freshmen and seniors in predicting math performance from the attitudes toward math scale? 4. If the Y-intercepts do not differ significantly, then what is (or what would be) the \"common\" regression equation that can be used for both (or either) high school freshmen and seniors in predicting math performance from the math attitudes? Justify your decision using information from your output. Please answer this question regardless of your decisions in any prior questions. 5. As a researcher, which regression equation(s) would you choose to interpret your data and your findings? In other words, which model best describes your data? Briefly explain how you came to this conclusion and then write a short narrative as if you were interpreting the results for the principal or administrator of the school in which this data was collected (Note: assume that he has not had any statistical training). 6. Calculate the adjusted standardized math assessment score for high school freshmen and then for seniors after controlling for the variability associated with the attitudes toward math scale. In other words, after statistically equating the freshmen and seniors on the attitudes towards math scale, are there significant differences in the standardized math assessment between the two groups? Are the high school freshmen and senior adjusted means significantly different from each other? What information did you use to answer this statistical question? $FL2@(#) IBM SPSS STATISTICS 64-bit MS Windows 22.0.0.0 #########################Y@06 Dec 1614:28:11 ###########################AGE ####age of student ########################MATH "###math standardized assessment score ########################ATTITUDE,###student positive attitude toward mathematics#################Freshmen ######?#Senior ######################################################################### ############ ######################################################AGE=Age MATH=Math ATTITUDE=attitude###########################################8###Age: $@Role('0' )/Math:$@Role('0' )/attitude:$@Role('0' )################UTF-8#######ddd\\(\\#@p= @ddd#@#@#######@ddUUUUUU#@#######@UUUUUU#@ddd(\\# @#######@iddid)\\(#@ddR#Q#@UUUUUU#@######! @ddd#@UUUUUU#@ddd#######@#Q##@ p= #@ddUUUUUU#@UUUUUU#@(\\#@ddd#@#######@jddd#@UUUUUU #@ddUUUUUU#@UUUUUU#@#@dddUUUUUU#@ @dddUUUUUU#@#@#@ddUUUUUU#@#@UUUUUU#@dddUUUUUU# @UUUUUU#@ddjd#######@\\(\\#@ddUUUUUU#@UUUUUU#@UUUUUU#@dddUUUUUU# @#######@ddid#@#######@ddUUUUUU#@UUUUUU#@#@ddd##### @#@ddd#@* @#######@ddj#@######!@ddd @######!@ddd#@UUUUUU#@#######@ddUUUUUU"@UUUUUU @UUUUUU! @djddUUUUUU#@iddd#@#@ddUUUUUU#@#@UUUUUU#@ddld UUUUUU#@dddUUUUUU#@Q# @(\\B @ddp= @Q#!@(\\"@dee#Q$@p= #@eee333333#@#Q#@z#G#@eep= #@(\\#@#@eee= p=#@\\(\\#@eee\\(\\#@{#Gz#@p= #@eep= #@#Q##@UUUUUU!@eee(\\#@p= #@eee#######@p= #@(\\#@ee(\\#@#@#@eeeUUUUUU@333333#@eee= p=#@Hz#G#@Q##@eeQ##@Q##@UUUUUU#@eeie*! @eeie#Q#@ p= #@eeR#Q#@UUUUUU#@#######@eee(\\#@UUUUUU#@eee\\(\\#@)\\( #@Q##@eep= #@UUUUUU!@L @eeeR#Q @(\\ @eee#Gz @#Gz##@p= #@ekeQ##@)\\(#@eee p= @#Q#@eee= p=#@#Q8!@#Q8!@eep= # @z#G @Q##@eee= p=!@q= @ eeeffffff!@33333 @!@ee#@Q#! @)\\(#@eee(\\u"@(\\#@eee#@\\( @(\\# @e### p= #@#Q$@ 1)a), 2), 3)a)b)c) Variables Entered/Removeda Model Variables Variables Entered Removed Method age of student, 1 student positive . Enter attitude toward mathematicsb a. Dependent Variable: math standardized assessment score b. All requested variables entered. Model Summary Model R 1 .721 R Square a Adjusted R Std. Error of the Square Estimate .520 .514 10.33846 a. Predictors: (Constant), age of student, student positive attitude toward mathematics ANOVAa Model 1 Sum of Squares df Mean Square Regression 18955.999 2 9478.000 Residual 17528.935 164 106.884 Total 36484.934 166 F Sig. .000b 88.676 a. Dependent Variable: math standardized assessment score b. Predictors: (Constant), age of student, student positive attitude toward mathematics Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B (Constant) 1 student positive attitude toward mathematics age of student Std. Error 17.553 4.220 5.782 .618 11.992 1.640 a. Dependent Variable: math standardized assessment score Beta 4.160 .000 .518 9.349 .000 .405 7.313 .000 1)b)i) Variables Entered/Removeda Model 1 Variables Variables Method Entered Removed attitude_freshm . Enter enb a. Dependent Variable: math_freshmen b. All requested variables entered. Model Summary Model R R Square .549a 1 Adjusted R Std. Error of the Square Estimate .301 .293 11.22836 a. Predictors: (Constant), attitude_freshmen ANOVAa Model Sum of Squares Regression 1 df Mean Square F 4723.587 1 4723.587 Residual 10968.615 87 126.076 Total 15692.202 88 Sig. .000b 37.466 a. Dependent Variable: math_freshmen b. Predictors: (Constant), attitude_freshmen Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B 1 (Constant) attitude_freshmen a. Dependent Variable: math_freshmen Std. Error 20.626 5.845 5.316 .869 Beta .549 3.529 .001 6.121 .000 1)b)ii) Variables Entered/Removeda Model 1 Variables Variables Entered Removed attitude_seniorb Method . Enter a. Dependent Variable: math_senior b. All requested variables entered. Model Summary Model R R Square .649a 1 Adjusted R Std. Error of the Square Estimate .421 .414 9.22659 a. Predictors: (Constant), attitude_senior ANOVAa Model 1 Sum of Squares df Mean Square Regression 4709.578 1 4709.578 Residual 6469.870 76 85.130 11179.449 77 Total F Sig. .000b 55.322 a. Dependent Variable: math_senior b. Predictors: (Constant), attitude_senior Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B 1 (Constant) attitude_senior a. Dependent Variable: math_senior Std. Error 24.586 6.308 6.477 .871 Beta .649 3.897 .000 7.438 .000 4) Variables Entered/Removeda Model Variables Variables Entered Removed Method student positive 1 attitude toward . Enter mathematicsb a. Dependent Variable: math standardized assessment score b. All requested variables entered. Model Summary Model R R Square .602a 1 Adjusted R Std. Error of the Square Estimate .363 .359 11.86911 a. Predictors: (Constant), student positive attitude toward mathematics ANOVAa Model 1 Sum of Squares df Mean Square Regression 13240.449 1 13240.449 Residual 23244.485 165 140.876 Total 36484.934 166 F Sig. .000b 93.987 a. Dependent Variable: math standardized assessment score b. Predictors: (Constant), student positive attitude toward mathematics Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B (Constant) 1 student positive attitude toward mathematics Std. Error 16.660 4.843 6.731 .694 a. Dependent Variable: math standardized assessment score Math = 16.66 + 6.731* attitude Beta .602 3.440 .001 9.695 .000 6) Between-Subjects Factors Value Label age of student N .00 Freshmen 89 1.00 Senior 78 Tests of Between-Subjects Effects Dependent Variable: math standardized assessment score Source Type III Sum of df Mean Square F Sig. Squares 18955.999a 2 9478.000 88.676 .000 Intercept 3173.293 1 3173.293 29.689 .000 attitude 9342.716 1 9342.716 87.410 .000 Age 5715.550 1 5715.550 53.474 .000 Error 17528.935 164 106.884 Total 694152.000 167 36484.934 166 Corrected Model Corrected Total a. R Squared = .520 (Adjusted R Squared = .514) 1)a), 2), 3)a)b)c) Variables Entered/Removeda Model Variables Variables Entered Removed Method age of student, 1 student positive . Enter attitude toward mathematicsb a. Dependent Variable: math standardized assessment score b. All requested variables entered. Model Summary Model R 1 .721 R Square a Adjusted R Std. Error of the Square Estimate .520 .514 10.33846 a. Predictors: (Constant), age of student, student positive attitude toward mathematics ANOVAa Model 1 Sum of Squares df Mean Square Regression 18955.999 2 9478.000 Residual 17528.935 164 106.884 Total 36484.934 166 F Sig. .000b 88.676 a. Dependent Variable: math standardized assessment score b. Predictors: (Constant), age of student, student positive attitude toward mathematics Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B (Constant) 1 student positive attitude toward mathematics age of student Std. Error 17.553 4.220 5.782 .618 11.992 1.640 a. Dependent Variable: math standardized assessment score Beta 4.160 .000 .518 9.349 .000 .405 7.313 .000 1)b)i) Variables Entered/Removeda Model 1 Variables Variables Method Entered Removed attitude_freshm . Enter enb a. Dependent Variable: math_freshmen b. All requested variables entered. Model Summary Model R R Square .549a 1 Adjusted R Std. Error of the Square Estimate .301 .293 11.22836 a. Predictors: (Constant), attitude_freshmen ANOVAa Model Sum of Squares Regression 1 df Mean Square F 4723.587 1 4723.587 Residual 10968.615 87 126.076 Total 15692.202 88 Sig. .000b 37.466 a. Dependent Variable: math_freshmen b. Predictors: (Constant), attitude_freshmen Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B 1 (Constant) attitude_freshmen a. Dependent Variable: math_freshmen Std. Error 20.626 5.845 5.316 .869 Beta .549 3.529 .001 6.121 .000 1)b)ii) Variables Entered/Removeda Model 1 Variables Variables Entered Removed attitude_seniorb Method . Enter a. Dependent Variable: math_senior b. All requested variables entered. Model Summary Model R R Square .649a 1 Adjusted R Std. Error of the Square Estimate .421 .414 9.22659 a. Predictors: (Constant), attitude_senior ANOVAa Model 1 Sum of Squares df Mean Square Regression 4709.578 1 4709.578 Residual 6469.870 76 85.130 11179.449 77 Total F Sig. .000b 55.322 a. Dependent Variable: math_senior b. Predictors: (Constant), attitude_senior Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B 1 (Constant) attitude_senior a. Dependent Variable: math_senior Std. Error 24.586 6.308 6.477 .871 Beta .649 3.897 .000 7.438 .000 4) Variables Entered/Removeda Model Variables Variables Entered Removed Method student positive 1 attitude toward . Enter mathematicsb a. Dependent Variable: math standardized assessment score b. All requested variables entered. Model Summary Model R R Square .602a 1 Adjusted R Std. Error of the Square Estimate .363 .359 11.86911 a. Predictors: (Constant), student positive attitude toward mathematics ANOVAa Model 1 Sum of Squares df Mean Square Regression 13240.449 1 13240.449 Residual 23244.485 165 140.876 Total 36484.934 166 F Sig. .000b 93.987 a. Dependent Variable: math standardized assessment score b. Predictors: (Constant), student positive attitude toward mathematics Coefficientsa Model Unstandardized Coefficients Standardized t Sig. Coefficients B (Constant) 1 student positive attitude toward mathematics Std. Error 16.660 4.843 6.731 .694 a. Dependent Variable: math standardized assessment score Math = 16.66 + 6.731* attitude Beta .602 3.440 .001 9.695 .000 6) Between-Subjects Factors Value Label age of student N .00 Freshmen 89 1.00 Senior 78 Tests of Between-Subjects Effects Dependent Variable: math standardized assessment score Source Type III Sum of df Mean Square F Sig. Squares 18955.999a 2 9478.000 88.676 .000 Intercept 3173.293 1 3173.293 29.689 .000 attitude 9342.716 1 9342.716 87.410 .000 Age 5715.550 1 5715.550 53.474 .000 Error 17528.935 164 106.884 Total 694152.000 167 36484.934 166 Corrected Model Corrected Total a. R Squared = .520 (Adjusted R Squared = .514)