Question

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

X:	−7	−16	13	3	16
Y:	54	241	157	1	342

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

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.)

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	9	795	722.8	76206.0	1851.00
mean	1.80	159.00	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   1.80   ,     ȳ = Σy/n =   159.00  
                  
SSxx =    Σ(x-x̅)² =    722.8000          
SSxy=   Σ(x-x̅)(y-ȳ) =   1851.0          
                  
estimated slope , ß1 = SSxy/SSxx =   1851.0   /   722.800   =   2.5609
                  
intercept,   ß0 = y̅-ß1* x̄ =   154.3904          
                  
so, regression line is   Ŷ =   154.3904   +   2.5609   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    71465.822          
                  
std error ,Se =    √(SSE/(n-2)) =    154.344          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.249   

2)

Yes but weak positive

3)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	739	795	52890.8	76206.0	60935.00
mean	147.80	159.00	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   147.80   ,     ȳ = Σy/n =   159.00  
                  
SSxx =    Σ(x-x̅)² =    52890.8000          
SSxy=   Σ(x-x̅)(y-ȳ) =   60935.0          
                  
estimated slope , ß1 = SSxy/SSxx =   60935.0   /   52890.800   =   1.1521
                  
intercept,   ß0 = y̅-ß1* x̄ =   -11.2790          
                  
so, regression line is   Ŷ =   -11.2790   +   1.1521   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    6003.352          
                  
std error ,Se =    √(SSE/(n-2)) =    44.734          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.96

THANKS

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