Question

x	4	5	6	8	10
y	3.4	4.2	6.3	10.9	13.3

a) Use the (x', y') data points and a calculator with regression keys to find the least-squares equation y' = a + bx'. What is the correlation coefficient? (Use 3 decimal places.)

y'	= _____	+ _____ x'
r	=

b) Use the results of part (b) to find estimates for α and β in the power law y = αx^β. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. (Use 3 decimal places.)

α	= ____
β	= ____
	= ___	· x^ ____

Answer 1

1)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	33	38.1	23.2	74.3	41.14
mean	6.60	7.62	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   6.60   ,     ȳ = Σy/n =   7.62  
                  
SSxx =    Σ(x-x̅)² =    23.2000          
SSxy=   Σ(x-x̅)(y-ȳ) =   41.1          
                  
estimated slope , ß1 = SSxy/SSxx =   41.1   /   23.200   =   1.7733
                  
intercept,   ß0 = y̅-ß1* x̄ =   -4.0836          
                  
so, regression line is   Ŷ =   -4.084 +   1.773 *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    1.315          
                  
std error ,Se =    √(SSE/(n-2)) =    0.662          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.991   

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