Question

Here is data with y as the response variable.

x	y
43.2	52.4
52.8	58.7
52.5	48.6
189.8	112.4
64.6	49.8
47.6	57.2
31.4	36.4
66.6	60.1

Make a scatter plot of this data. Which point is an outlier?

Enter as an ordered pair. For example (a,b) - with parenthesis.


Find the regression equation for the data set without the outlier.


Enter as an equation of the form y=a+bxy=a+bx. Rounded to three decimal places. For this WAMAP question, do not include the hat in y-hat.


Find the regression equation for the data set with the outlier.


Enter as an equation of the form y=a+bxy=a+bx. Rounded to three decimal places. For this WAMAP question, do not include the hat in y-hat.

Is this outlier an influential point? An influential point, when removed from the data, will change the regression equation drastically.

• No, the outlier does not appear to be an influential point.
• Yes, the outlier appears to be an influential point.

Answer 1

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

(43.2, 52.4)
(52.8 , 58.7)
(52.5 , 48.6)

(189.8 ,112.4
(64.6 , 49.8)
(47.6 , 57.2)
(31.4 , 36.4)
(66.6 , 60.1)
)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	358.7	363.2	889.9571429	397.4	388.55
mean	51.24	51.89	SSxx	SSyy	SSxy

sample size ,   n =   7          
here, x̅ = Σx / n=   51.24   ,     ȳ = Σy/n =   51.89  
                  
SSxx =    Σ(x-x̅)² =    889.9571          
SSxy=   Σ(x-x̅)(y-ȳ) =   388.6          
                  
estimated slope , ß1 = SSxy/SSxx =   388.6   /   889.957   =   0.4366
                  
intercept,   ß0 = y̅-ß1* x̄ =   29.5131          
                  
so, regression line is   Ŷ =   29.513   +   0.437   *x
.............

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	548.2	475.6	17615.615	3601.6	7709.27
mean	68.53	59.45	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ = Σx / n=   68.53   ,     ȳ = Σy/n =   59.45  
                  
SSxx =    Σ(x-x̅)² =    17615.6150          
SSxy=   Σ(x-x̅)(y-ȳ) =   7709.3          
                  
estimated slope , ß1 = SSxy/SSxx =   7709.3   /   17615.615   =   0.4376
                  
intercept,   ß0 = y̅-ß1* x̄ =   29.4608          
                  
so, regression line is   Y =   29.461   +   0.438   *x

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

                  

• No, the outlier does not appear to be an influential point.

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

THANKS

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