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Multiple Linear Regression Assignment




Question;Multiple Linear Regression1 Relationship Between Eighth Grade IQ, Eighth Grade Abstract Reasoning and Ninthgrade Math Score For a statistics class project, students examined the relationship between x 1 = 8thgrade IQ, x2 = 8th grade Abstract Reasoning and y = 9th grade math scores for 20 students. The data aredisplayed below.Student1234567891011121314151617181920Math Score3331353841373739434041444045484531474348IQ95100100102103105106106106109110110111112112114114115117118Abstract Reas2824293033323436383940434142464441474249Open the dataset IQ found in the Datasets folder in ANGEL. Perform a linear regression with theResponse (dependent variable) math score and the variables IQ and Abstract_Reas as the Predictors(independent variables). Store/Save the (unstandardized) Residuals and Fitted(Predicted) values.The output should look as follows:MINITAB: Regression Analysis: Math Score versus IQ, Abstract_ReasThe regression equation isMath Score = 54.1 - 0.484 IQ + 1.02 Abstract_ReasPredictorConstantIQAbstract_ReasS = 3.00271Coef54.05-0.48361.0185SE Coef22.990.29550.2656R-Sq = 70.5%T2.35-1.643.84P0.0310.1200.001R-Sq(adj) = 67.1%Analysis of VarianceSourceRegressionDF2SS366.92MS183.46F20.35P0.0001Residual ErrorTotal1719153.28520.209.02SPSS: Regression Analysis: Math Score versus IQ, Abstract_ReasModel SummarybModelRR Square.840aStd. Error of theSquare1Adjusted REstimate.705.6713.003a. Predictors: (Constant), Abstract_Reas, IQb. Dependent Variable: MathScoreANOVAaModelSum of SquaresdfMean SquareRegression2183.462Residual153.27617520.200Sig..000b9.016Total1366.924F20.34819a. Dependent Variable: MathScoreb. Predictors: (Constant), Abstract_Reas, IQCoefficientsaModelUnstandardized CoefficientsStandardizedtSig.CoefficientsB(Constant)Std. Error22.991IQ-.484.296Abstract_Reas154.0531.019.266Beta2.351.031-.573-1.636.1201.3433.835.001a. Dependent Variable: MathScorea. What is the regression equation and provide an interpretation of each slope in terms of the change in Yper unit change in X?b. Create two scatter plots of the measurements by selecting math score as the response (y-axis), IQ andabstract reasoning as the predictors (x-axis) Describe the relationship between math score and IQ andmath score and abstract reasoning.c. Based on the output, what is the test of the slopes for this regression equation? That is, provide the nulland alternative hypotheses, the test statistic, p-value of the test, and state your decision and conclusion.2d. From the output, what is the meaning of the ANOVA F-test? Provide the two hypotheses (Ho and Ha)statements, decision and conclusion.e. Check assumptions of constant variance (a scatterplot of the residuals versus the fits(predicted) values)and normality (Minitab a probability plot or SPSS a Q-Q plot in SPSS). What are your conclusionsbased on these graphs?MINITAB: Scatterplot by Graph > Scatter Plot > Simple. Probability plot by Graph > ProbabilityPlot > SingleSPSS Users: Scatterplot by Graphs > Legacy Dialogues > Scatter/Dot > Simple Scatter Q-Q plot byAnalyze > Descriptive Statistics > Explore and enter Unstandardized Residuals in Dependent Listclick Plots and select box for Normal plots with tests


Paper#61543 | Written in 18-Jul-2015

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