Question

Question 2. The following variables were collected for a random sample of 10 students. Based on information below, identify and interpret least-squares regression equation. Also, identify and interpret the strength, PRE, direction, and significance of the association between the dependent and independent variable at the alpha level of 0.05. Show five steps if relevant. Obtain all the relevant statistics. Provide a brief overall conclusion. (10 marks) Hours of watching TV a day (X). 6 5 12 10 7 5 6 10 11 10 Exam score (V) 88 56 45 42 55 77 61 37 26 15

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	82.00	502.00	63.60	4413.60	-406.40
mean	8.20	50.20	SSxx	SSyy	SSxy

Sample size,   n =   10      
here, x̅ = Σx / n=   8.200          
ȳ = Σy/n =   50.200          
SSxx =    Σ(x-x̅)² =    63.6000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -406.4      
              
estimated slope , ß1 = SSxy/SSxx =   -406.4/63.6=   -6.3899      
intercept,ß0 = y̅-ß1* x̄ =   50.2- (-6.3899 )*8.2=   102.5975      
              
Regression line is, Ŷ=   102.60   + (   -6.390   )*x

..............

              
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    1816.7296      
std error ,Se =    √(SSE/(n-2)) =    15.0695      

..............

              
correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.7671   

THERE IS NEGATIVE RELATIONSHP BETWEEN TWO VARIABLES

MODERATE STRENGTH

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Ho:   β1=   0
H1:   β1╪   0
n=   10  
alpha =   0.05  
estimated std error of slope =Se(ß1) = Se/√Sxx =    15.0695/√63.6=   1.8896
t stat = estimated slope/std error =ß1 /Se(ß1) =    (-6.3899-0)/1.8896=   -3.38

Degree of freedom ,df = n-2=   8  

      
p-value =    0.0096  
decison :    p-value<α , reject Ho  
Conclusion:   Reject Ho and conclude that slope is significantly different from zero  

THERE IS SIGNIFCANT RELATIONSHIP BETWEEN TWO VARIABLES

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SO, HERE

WE can cconcude that there is signifcant association between two variables

and there is negative relation with moderate strength

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Please let me know in case of any doubt.

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