Question

U1 100,000, and Merent ways in which the winners els are not replaces after they are drawn) 20 points) An educator wants to see how the number of absences for a student in her class affects the student's final grade. The data obtained from a sample a shown below: No. of absences x 10 12 04 96 65 Final grade y 70 Round final calculations to three (3) decimal points, Compute the correlation coefficient, r= Write an equation of the line that best fits this data

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
10	70	14.69	106.78	-39.61
12	65	34.03	235.11	-89.44
2	96	17.36	245.44	-65.28
0	94	38.03	186.78	-84.28
8	75	3.36	28.44	-9.78
5	82	1.36	2.78	-1.94

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	37	482	108.8333333	805.333	-290.333
mean	6.167	80.333	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.981
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sample size ,   n =   6          
here, x̅ = Σx / n=   6.17   ,     ȳ = Σy/n =   80.33  
                  
SSxx =    Σ(x-x̅)² =    108.8333          
SSxy=   Σ(x-x̅)(y-ȳ) =   -290.3          
                  
estimated slope , ß1 = SSxy/SSxx =   -290.3   /   108.833   =   -2.66769
                  
intercept,   ß0 = y̅-ß1* x̄ =   96.78407          
                  
so, regression line is   Ŷ =   96.784 - 2.668*x