Question

Given Information:

n=500

independent variable = drug dosage -> 400mg avg w/ stdv 75mg

dependent variable = days to recovery -> 10 days avg w/ stdv 3 days

* correlation coefficient is .65

stdv = sqrt of sample variance

Can you calculate the following:

x bar, y bar, Sxx, Syy, rxy, Sxy, β0, β1, SSR, SSE, s2

ANOVA Table

Answer 1

here, x̅ = Σx / n=   400.000   ,

    ȳ = Σy/n =   10.000

SSxx = s²*(n-1) = 75^2*499 = 2806875.00

SSyy = 3² * 499 = 4491.00

r = 0.65

SSxy = r*Sx*Sy*(n-1) = 0.65*75*3*499 = 72978.75

estimated slope , ß1 = SSxy/SSxx =   72978.8   /   2806875.000   =   0.0260
                  
intercept,   ß0 = y̅-ß1* x̄ =   -0.40000          

SSR=   S²xy/Sxx =   1897.4475
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    2593.55250000
estimate of variance,   Se² = SSE/(n-2) =    5.208

Anova table
variation	SS	df	MS	F-stat	p-value
regression	1897.45	1	1897.4475	364.3377	0.0000
error,	2593.55	498	5.2079
total	4491.000	499

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