a) Find the sample correlation coefficient r between the league positions in 2008 and 2009. Test the null hypothesis that the population correlation coefficient p between the league positions in 2008 and 2009 is zero.
b) Obtain an approximate 95% confidence interval for the population correlation coefficient between the league positions in 2008 and 2009. Comment.
c) State the assumptions of the simple linear regression model.
d) Fit a simple linear regression model to the data in Table 1.1 to explain the league position in 2009 as linear function of the league position in 2008.
e) Calculate the percentage of variation of y explained by x.
f) Obtain the fitted value, residual and standardized residual for Leicester. Comment.

a) Mean of x: (7+1+10+4...+2)/11=6
SSx=(7-6)^2+(1-6)^2+...+(2-6)^2=110
Mean of y: (1+2+3+...+11)/11=6
SSy=(1-6)^2+(2-6)^2+...+(11-6)^2=110
Sxy=(1-6)*(7-6)+(2-6)*(1-6)+...+(2-6)*(11-6)=-7
r=Sxy/sqrt(SSx*SSy)=-7/sqrt(110*110)=-0.06364
Null hypothesis: r=0
Alternative hypothesis: r<0
This is one tailed t test.
The degree of freedom is n-2=11-2=9.
The critical t value is -1.83
Test value t=r*sqrt((n-2)/(1-r^2))=-0.06364*sqrt((11-2)/(1-0.06364^2))=-0.19
Since -0.19>-1.83, we could not reject null hypothesis.
Based on the test, we could conclude that population correlation coefficient between the ...

Solution Summary

The linear statistical models and hypothesis testings is examined.

... The explanatory power of the model can be examined ... are dealing with a simple linear regression analysis ... Thus two equivalent statistical tests can be performed. ...

... coefficient* Mann-Kendall rank correlation statistics* Trend testing... o Further reading o Exercises Linear Regression I ... o A few words on modelling strategy ...

... not have significant contribution to the regression model. ... should have a positive linear relationship with ACT ... Regression Statistics Multiple R 0.7598 R Square ...

... picture that variables have any linear relationship, the ... study using the various statistical models, it can be ... context for the problem, model development, data ...

... You obtain the following regression statistics for the ...Model Unstandardized Coefficients Standardized Coefficients t Sig ... this is simple linear regression (only ...

Statistics Problem Set: Regression and Linear Programming. ... c. The linear program exhibits unfeasibility. ... coefficients of the regression model are significantly ...

... 5 residuals of the model (that is, vertical ... an estimation of the linear regression parameters. ... We described two methods for testing the Statistical Hypothesis. ...

Fuel Consumptions Case (Multiple Linear Regression): Calculate confidence intervals. ... (Fig-1a) t Statistics and p ... significantly related to y in the model with a ...

... The linear model can explain 87.78% of the variability ... be better than straight line model in describing ... Regression Statistics Multiple R 0.947598178 R Square ...