Question

The table below is from 12 randomly selected women. They were asked to record their height in inches and their shoe size. Height (inches) 67 66 64 64 67 64 68 65 68 65 66 61 Shoe Size | 10 7 2 8 8.5 8.5 8.5 9875 tell us about the linear regression line? a) Calculate the r. r and the linear regression line. What do the r and b) Predict the shoe size of a women who is 54" tall. Calculate the residual for a women 61 inches tall.

show work please

Answer 1

a] X Values
∑ = 785
Mean = 65.417
∑(X - Mx)2 = SSx = 44.917

Y Values
∑ = 97
Mean = 8.083
∑(Y - My)2 = SSy = 12.917

X and Y Combined
N = 12
∑(X - Mx)(Y - My) = 14.083

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 14.083 / √((44.917)(12.917)) = 0.5847

r is showing positive and moderate correlation coefficient between two variables.

r^2= (0.5847)^2= 0.3419

It indicates that the model explains 34.19% of the variability of the response data around its mean

b] Sum of X = 785
Sum of Y = 97
Mean X = 65.4167
Mean Y = 8.0833
Sum of squares (SSX) = 44.9167
Sum of products (SP) = 14.0833

Regression Equation = ŷ = bX + a

b = SP/SSX = 14.08/44.92 = 0.31354

a = MY - bMX = 8.08 - (0.31*65.42) = -12.42764

ŷ = 0.31354X - 12.42764

X= 5feet 4 inches in inches = 64.8

ŷ = 0.31354*64.8 - 12.42764

ŷ = 7.89

c] ŷ = 0.31354X - 12.42764

X=61 inches

ŷ = 0.31354*61 - 12.42764

ŷ = 6.698

Residual= y(hat)-y= 6.698-6= 1.698