Question

1. As a result of running a simple regression on a data set, the following estimated regression equation was obtained:

      = 9.7 + 13.4x

Furthermore, it is known that SST = 622, and SSE = 150.

2. You are given the following information about y and x:

	y	x
	Dependent Variable	Independent Variable
	11	6
	15	5
	10	2
	14	2

Linear regression using least squares method yielded the following equation:
  = 12.06 + 0.12x

What is the predicted value of y when x = 1? Round your answer to two decimal places.

Calculate the correlation coefficient R; round your answer to three decimal places.

3. You are given the following information about variables y and x:

	y	x
	Dependent Variable	Independent Variable
	-10.0	-9.1
	8.2	-7.8
	-5.5	6.4
	10.3	-9.0

In addition, it is known that the slope of the regression line b₁= -6.6
The y-intercept b₀for the estimated regression equation equals ____ (round your answer to two decimal places).

Answer 1

2)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	15	50	12.75	17.0	1.50
mean	3.75	12.50	SSxx	SSyy	SSxy

sample size ,   n =   4          
here, x̅ = Σx / n=   3.75   ,     ȳ = Σy/n =   12.50  
                  
SSxx =    Σ(x-x̅)² =    12.7500          
SSxy=   Σ(x-x̅)(y-ȳ) =   1.5          
                  
estimated slope , ß1 = SSxy/SSxx =   1.5   /   12.750   =   0.1176
                  
intercept,   ß0 = y̅-ß1* x̄ =   12.0588          
                  
so, regression line is   Ŷ =   12.0588   +   0.117647   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    16.8          
                  
std error ,Se =    √(SSE/(n-2)) =    2.90          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.102   

Predicted Y at X=   1   is                  
Ŷ =   12.05882   +   0.117647   *   1   =   12.18

3)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	-19.5	3	170.5475	301.3	-86.24
mean	-4.88	0.75	SSxx	SSyy	SSxy

sample size ,   n =   4          
here, x̅ = Σx / n=   -4.88   ,     ȳ = Σy/n =   0.75  
                  
SSxx =    Σ(x-x̅)² =    170.5475          
SSxy=   Σ(x-x̅)(y-ȳ) =   -86.2          
                  
estimated slope , ß1 = SSxy/SSxx =   -86.2   /   170.548   =   -0.5056
                  
intercept,   ß0 = y̅-ß1* x̄ =   -1.72   

THANKS

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