Question

Neck (Y)	Waist (X)
13	30
14	36
12	28
14	27
15	28
15	33
16	36
13	31
16	40
13	30
14	37
13	33
14	35
12	24
14	35
15	35
17	43
14	36
13	29
13	31

* If you are able to can you please type out and number the answers to each one so it's easier to understand. Thank you!

1) T-statistic, degree of freedom and P-value (assume a=0.05)

2) Explain the meaning of a, b, r, and r^2 in this study

3) Within the domain, pick some value not used for the explanatory variables and interpolate the response (show basic calculations)

4) Outside the domain, pick some value of the data and extrapolate the response (show basic calculations)

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	657.00	280.00	412.55	34.00	89.00
mean	32.85	14.00	SSxx	SSyy	SSxy

sample size ,   n =   20          
here, x̅ = Σx / n=   32.850   ,     ȳ = Σy/n =   14.000  
                  
SSxx =    Σ(x-x̅)² =    412.5500          
SSxy=   Σ(x-x̅)(y-ȳ) =   89.0          
                  
estimated slope , ß1 = SSxy/SSxx =   89.0   /   412.550   =   0.2157
                  
intercept,   ß0 = y̅-ß1* x̄ =   6.91322          
                  
so, regression line is   Ŷ =   6.91   +   0.216   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    14.7999          

a)

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   20              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    0.907   /√   412.55   =   0.0446
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    0.2157   /   0.0446   =   4.8324
                  
t-critical value=    2.1009   [excel function: =T.INV.2T(α,df) ]          
Degree of freedom ,df = n-2=   18              
p-value =    0.000133627              
decison :    p-value<α , reject Ho              
Conclusion:   Reject Ho and conclude that slope is significantly different from zero              

2)

a= intercept=6.91322

b=slope = 0.216

r= correlation = 0.7515

r²= coefficent of determination = 0.5647

3)

let X=14

Predicted Y at X=   14   is          
Ŷ =   6.9132   +   0.2157   *14=   9.933

4)

let X=20

Predicted Y at X=   20   is          
Ŷ =   6.9132   +   0.2157   *20=   11.228