Question

Scartter plot of Birth 15to17 vs Poverty Rate 40 30 20 10 10 15 20 25 Please use summary statistics below to answer following questions n = 51, { x = 669, { x2 = 9690.44, n = 1136.4, E x2 = 28556.56, 2 xi) = 16163.14

Thank you!!!

Answer 1

a)

	X	Y	XY	X²	Y²
total sum	669.000	1136.400	16163.14	9690.440	28557
mean	13.1176	22.2824

sample size ,   n =   51          
here, x̅ =Σx/n =   13.1176   ,   ȳ = Σy/n =   22.28235294  
                  
SSxx =    Σx² - (Σx)²/n =   914.734          
SSxy=   Σxy - (Σx*Σy)/n =   1256.246          
SSyy =    Σy²-(Σy)²/n =   3234.894          
estimated slope , ß1 = SSxy/SSxx =   1256.246   /   914.734   =   1.3733
                  
intercept,   ß0 = y̅-ß1* x̄ =   4.2673          
                  
so, regression line is   Ŷ =   4.27   +   1.37   *x

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

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.7303
      
R² =    (Sxy)²/(Sx.Sy) =    0.533
............

r: relationship between x and y is moderate, positve and linear

53.3% data can be explained by x of Y

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

Anova table
variation	SS	df	MS	F-stat	p-value
regression	1725.259	1	1725.259	55.999	0.0000
error,	1509.635	49	30.809
total	3234.894	50

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

p value < 0.05

so modal is significant

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

slope hypothesis test               tail=   2
Ho:   ß1=   0          
H1:   ß1╪   0          
n=   51              
alpha=   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    5.551   /√   915   =   0.1835
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    1.3733   /   0.1835   =   7.483
                  
  
Degree of freedom ,df = n-2=   49              
p-value =    0.0000              
decision :    p-value<α , reject Ho              
Conclusion:   Reject Ho and conclude that slope is significantly different from zero          

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

   

THANKS

revert back for doubt

please upvote