Question

Given the following sample observations, draw a scatter diagram on a separate piece of paper.

X:	−7	−16	11	1	16
Y:	50	248	155	3	343

1. Compute the correlation coefficient. (Round your answer to 3 decimal places.)

Coefficient of correlation ________

2. Does the relationship between the variables appear to be linear?

• Yes

• No

3. Try squaring the x variable and then determine the correlation coefficient. (Round your answer to 3 decimal places.)

Coefficient of correlation ______

Answer 1

1)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	5	799	678	78006.8	2079.00
mean	1.00	159.80	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   1.00   ,     ȳ = Σy/n =   159.80  
                  
SSxx =    Σ(x-x̅)² =    678.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   2079.0          
                  
estimated slope , ß1 = SSxy/SSxx =   2079.0   /   678.000   =   3.0664
                  
intercept,   ß0 = y̅-ß1* x̄ =   156.7336          
                  
so, regression line is   Ŷ =   156.7336   +   3.0664   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    71631.813          
                  
std error ,Se =    √(SSE/(n-2)) =    154.523          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.286   

2)

Yes there does seems to very weak linear correlation.

3)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	683	799	54817.2	78006.8	63360.60
mean	136.60	159.80	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   136.60   ,     ȳ = Σy/n =   159.80  
                  
SSxx =    Σ(x-x̅)² =    54817.2000          
SSxy=   Σ(x-x̅)(y-ȳ) =   63360.6          
                  
estimated slope , ß1 = SSxy/SSxx =   63360.6   /   54817.200   =   1.1559
                  
intercept,   ß0 = y̅-ß1* x̄ =   1.9105          
                  
so, regression line is   Ŷ =   1.9105   +   1.1559   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    4771.289          
                  
std error ,Se =    √(SSE/(n-2)) =    39.880          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.969

THANKS

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