Question 1Based on the SPSS1. Based on descriptive statistics,Descriptive StatisticsMean Std. Deviation Nmath achievement test 12.5645 6.67031 75motivation scale 2.8744 .63815 73competence scale 3.2945 .66450 73fathers education 4.73 2.830 73mothers education 4.11 2.240 75gender .55 .501 75pleasure scale 3.1300 .60454 75grades in h.s. 5.68 1.570 75a. Checking on assumptions1. Correlations Statistics above 0.3Statistics Value Sig Value Alpha-value CorrelationMaths achievement x motivation scale .316 0.003 0.05 CorrelatedMaths achievement x competence .570 0.002 0.05 CorrelatedMaths achievement x father’s .381 0.000 0.05 CorrelatedMaths achievement x mother’s .338 0.002 0.05 CorrelatedMaths achievement x gender -.301 0.004 0.05 CorrelatedMaths achievement x pleasure .085 0.234 0.05 x CorrelatedSo, only maths achievement has no correlation with pleasure
2. Check on multicollinearity – Look on CoefficientTolerance value must be more than .1.So, there is no multicollinearity.3. Check on outliers, normality, linearity, homoscedaticity, independence of residualsSo, no major diversion from normality.b. . Look at Model SummaryModel SummarybModel R R Square Adjusted RSquareStd. Error of theEstimate1 .680a.462 .403 5.15575Collinearity StatisticsTolerance VIF.639 1.566.581 1.722.501 1.997.491 2.038.870 1.149.834 1.199
a. Predictors: (Constant), grades in h.s., motivation scale, motherseducation, pleasure scale, gender, competence scale, fatherseducationb. Dependent Variable: math achievement testR = .68, R squared = 0.462= 46.2% variance in mathematics achievement5. HypothesisHo – There is no statistical significance in the multiple regression.Ha – There is statistical significance in the multiple regression.Test statistics Sig Value Alpha-value DecisionF =7.738 0.000 0.05 Able to reject Ho, Accept HaSo, There is statistical significance in F (7,63) = 7.738, p<0.05.c. Look at independent variablesBeta must be the biggestModel Standardized Coefficients t Sig.Beta1(Constant) -1.792 .078motivation scale .163 1.412 .163competence scale .029 .225 .823fathers education .120 .878 .383mothers education .078 .592 .556gender -.275 -2.690 .009pleasure scale .091 .873 .386grades in h.s. .473 4.438 .000So, grades in high school has the strongest unique contribution towards mathematicsachievement, p<0.05.
Report:A standard multiple regression has been used to analyze the combination of motivation, competence,pleasure, grades in high school, father’s education, mother’s education and gender predict mathematicsachievement. Based on the descriptive statistics, the highest mean is the grades in high school which is5.68. The data screen has showed that the combination are correlated with each other except forpleasure with mathematics achievement. Further normality test shows that there is no major diversionas well as there is no multicollinearity within the independent variables.Regression results indicate an overall model of two predictors (gender and grades in high school)significantly predicted mathematics achievement R squared = 0.462, F (7, 63) = 7.738, p<0.05. Therefore,the model which includes grades and gender explains 46.2 % of the variance in the mathematicsachievement. Of these two variables, grades in high school makes the largest contribution (beta = 0.473)while gender makes has a beta = -.2755. The beta values also indicate the increase of standard deviation1.57 in grades, maths achievement statistics will also increase by 6.6.