7
MATHEMATICS
InstitutionAffiliation
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 
Pvalue 
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
_{}
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. Rsquared 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 Rsquared. 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
_{}
_{}
_{}
_{}
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 r^{2}is 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 
Pvalue 
Intercept 
43.131148 
25.123054 
1.7167956 
0.1611534 
X 
3.4918033 
3.8537005 
0.906091 
0.4161328 
_{}
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, r^{2}is 17.02%, higher than the previous r^{2}of 0.2%.
References
RamjiBalakrishnan, K. S. (2008). ManagerialAccounting.New York : John Wiley & Sons.
SharonLawner Weinberg, S. K. (2008). StatisticsUsing SPSS: An Integrative Approach.New York: Cambridge University Press.