Question

Here is data with y as the response variable. 55.1 79.1 76.4 43 79.3 65.2 69.7 42.7 77.5 61.9 15.9 146.6 66.6 87 90 75.6 65.2 84.9 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 equation of the form y = a ba Rounded to three decimal places Enter as an Preview 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 +ba. Rounded to three decimal places. Preview Do not include the hat in y-hat. Is this outlier an influential point? OYes, the outlier appears to be an influential point ONo, the outlier does not appear to be an influential point.

Answer 1

Scatterplot 160 140 120 100 80 60 40 20 20 40 60 0 80 100 X

Outlier = (15.9,146.6)

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without outlier

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
79.1	55.1	29.430625	123.766	-60.353125
76.4	43	7.425625	539.401	-63.288125
79.3	65.2	31.640625	1.051	-5.765625
69.7	42.7	15.800625	553.426	93.511875
77.5	61.9	14.630625	18.706	-16.543125
66.6	87	50.055625	431.601	-146.983125
75.6	90	3.705625	565.251	45.766875
65.2	84.9	71.825625	348.7556	-158.270625

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	589.4	529.8	224.515	2581.96	-311.925
mean	73.68	66.23	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ = Σx / n=   73.68   ,     ȳ = Σy/n =   66.23  
                  
SSxx =    Σ(x-x̅)² =    224.5150          
SSxy=   Σ(x-x̅)(y-ȳ) =   -311.9          
                  
estimated slope , ß1 = SSxy/SSxx =   -311.9   /   224.515   =   -1.3893
                  
intercept,   ß0 = y̅-ß1* x̄ =   168.5837          
                  
so, regression line is   Ŷ =   168.584   +   -1.389   *x

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with outlier

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
79.1	55.1	140.290864	402.225	-237.546914
76.4	43	83.620864	1033.980	-294.044691
79.3	65.2	145.068642	99.113	-119.909136
69.7	42.7	5.975309	1053.363	-79.335802
77.5	61.9	104.948642	175.710	-135.795802
15.9	146.6	2637.393086	5104.309	-3669.069136
66.6	87	0.429753	140.291	-7.764691
75.6	90	69.629753	220.3575	123.868642
65.2	84.9	4.225	94.954	-20.030

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	605.3	676.4	3191.582222	8324.30	-4439.628
mean	67.26	75.16	SSxx	SSyy	SSxy

sample size ,   n =   9          
here, x̅ = Σx / n=   67.26   ,     ȳ = Σy/n =   75.16  
                  
SSxx =    Σ(x-x̅)² =    3191.5822          
SSxy=   Σ(x-x̅)(y-ȳ) =   -4439.6          
                  
estimated slope , ß1 = SSxy/SSxx =   -4439.6   /   3191.582   =   -1.3910
                  
intercept,   ß0 = y̅-ß1* x̄ =   168.7109          
                  
so, regression line is   Ŷ =   168.711 +   -1.391 *x
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.8613  
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yes, the outlier appears to be an influential point