Question

data on x and 1697.80 Assume that the two (a) Intercept. (c) Mean

Answer 1

	X	Y	XY	X²	Y²
total sum	43	572.00	1697.8	157.42	23530
mean	3.0714	40.8571

sample size ,   n =   14      
here, x̅ =   3.071428571       ȳ =   40.85714286
              
SSxx =    Σx² - (Σx)²/n =   25.35      
SSxy=   Σxy - (Σx*Σy)/n =   -59.06      
SSyy =    Σy²-(Σy)²/n =   159.71      
slope ,    ß1 = SSxy/SSxx =   -2.33      

intercept,   ß0 = y̅-ß1* x̄ =   48.01

a)

intercept = 48.01

b)

slope = -2.33

c)

when X=3.1

Y= -2.33*3.1 + 48.01 = 40.79

d)

X Value   3.1
Confidence Level   95%

Sample Size , n=   14
Degrees of Freedom,df=n-2 =   12
critical t Value = 2.179

X̅ =    3.071
Σ(x-x̅)² =Sxx   25.349
Standard Error of the Estimate,Se=   1.3578
h Statistic = (1/n+(X-X̅)^2/Sxx) =    0.0715
Predicted Y (YHat) = 40.79
  
For Average Y  
margin of error,E=t*Se*√(1/n+(X-X̅)^2/Sxx) =    0.7908

Confidence Lower Limit=Ŷ -E = 40.00
Confidence Upper Limit=Ŷ +E =   41.58