## Mathematics

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7

MATHEMATICS

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Introduction

Thepaper shows the linear regression summary between the test scores andthe hours od preparation for five randomly selected students. Themultiple regressions help in establishing the correlation betweendependent variables and independent variables. The method also helpsin establishing the degree of the correlation. In the analysis, thetest score is the dependent variable and the hours of preparation isthe independent variable.

Question one

 SUMMARY OUTPUT Regression Statistics Multiple R 0.0479 R Square 0.002294 Adjusted R Square -0.33027 Standard Error 8.25288 Observations 5 ANOVA   df SS MS F Significance F Regression 1 0.469903 0.469903 0.006899 0.939034654 Residual 3 204.3301 68.11003 Total 4 204.8         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 74.8835 9.018608 8.303221 0.00366 46.18226101 103.5847 X -0.1068 1.285751 -0.08306 0.939035 -4.19863024 3.985038

Theregression model is in the form of



Where

Yis the dependent variable the test score

ais the constant.

Xis the hours of preparation

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Question two

Thecorrelation coefficient is 0.229%. The relationship between testscores and preparation time very weak and the model cannot be used topredict the test scores. R-squared is a measure of goodness of fit ofthe regression model. The extent to which the model can be reliedupon will depend on the value of R-squared. The regression model canbe relied upon to the extent of 0.229%.

Question three

Thebest predicted test score for a student who spent 7 hours preparingfor the test is as shown below







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Question four

Thestandard error for the model is shown by the regression equationabove the summary below shows the standard error for both theintercept and the independent variable.

   Coefficients Standard Error Intercept 74.8835 9.018607507 X -0.1068 1.285751191

Question five

At99%, the regression equation is as shown below









At99%, the score of a student who has spent seven hours preparing forthe exam is similar to at 95% confidence interval.

Question six

Thetotal variation in regression = Explained variation + Unexplainedvariation

Where

TheExplained Variation:

 X Y Estimated Y (based on the regression equation) Variation Total Explained Unexplained (Y – Y)^2 (Est. Y – Ŷ)^2 (Y – Est. Y)^2 5 64 74.35 104.04 0.0224 107.1 2 82 74.67 60.84 0.2208 53.7 9 72 73.92 4.84 0.0771 3.7 6 73 74.24 1.44 0.0018 1.5 10 80 73.82 33.64 0.1478 38.2   74.2   204.8 0.47 204.3

TheExplained Variation:

Fromthe computations above, the explained variation = 0.47

Question seven

Theunexplained variation is = 204.3 (detailed computations in theattached excel file)

Question eight

TheTotal Variation:

Where

Yis the test score

Ŷis the mean of the test score

Fromthe table above, the total variation is = 204.8.

Question nine

Fromthe regression equation computed earlier, the value of r2is 0.002294 or 0.2294%. This implies that only 0.2% of the changes inthe test score can be explained by the hours of preparation. The weakcorrelation is also explained by the small value of the explainedvariation compared to the total variation.

 Regression Statistics Multiple R 0.0479 R Square 0.002294

Question ten

Thenew regression equation is

 SUMMARY OUTPUT Regression Statistics Multiple R 0.4126703 R Square 0.1702968 Observations 6 ANOVA   df SS MS F Regression 1 619.79508 619.79508 0.8210009 Residual 4 3019.7049 754.92623 Total 5 3639.5       Coefficients Standard Error t Stat P-value Intercept 43.131148 25.123054 1.7167956 0.1611534 X 3.4918033 3.8537005 0.906091 0.4161328

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Thenew data point (3, 100) is an influential point since it improves theextent to which the test scores can be explained by the changes inhours of preparation. The correlation coefficient, r2is 17.02%, higher than the previous r2of 0.2%.

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References

RamjiBalakrishnan, K. S. (2008). ManagerialAccounting.New York : John Wiley &amp Sons.

SharonLawner Weinberg, S. K. (2008). StatisticsUsing SPSS: An Integrative Approach.New York: Cambridge University Press.

## Mathematics

• Uncategorized

2

Arational expression is defined as quotient of two polynomials. Arational expression cannot at any one time have its denominator equalto zero. Therefore, its domain is all the numbers which do not makethe denominator equal to zero. The domain expresses all the realnumbers with exceptions of undefined expressions. A rational functionis a fraction and from basics the denominator cannotbeequal to zero since it would be undefined. Finding the numbers thatmake an equation undefined involves creating an equation with thedenominator is not equals to zero.

Equation

Inthe equation, since M is in both the numerator and denominator, itcancels out to give

Thedenominator is a constant term. This implies that variable is absentsince it is impossible for 7 to be equated to zero. This implies thatthe domain do not have excludedvalues.It can be said that domain(D) comprises of a set of Real Numbers written as

D= {M| M ∈ℜ}