Question

5. A regression analysis is conducted with Xi = self-reported weight of an adult human Yi = measured weight of an adult human

Summary statistics n = 101 `Y = 5780/101 = 57.228 `X = 5731/101 = 56.743

A colleague has computed the following sums with the raw data: SUM (Xi -`X)*(Yi -`Y) = 4435.9 SUM (Xi -`X) = 4539.3

(a) Estimate the value of the coefficient ß0.

(b) Estimate the value of the coefficient ß1.

(c) Write the linear model in the form: Measured Weight = ß0 + ß0 x Self-Reported Weight

(d) Interpret the model in a realistic context.

Answer 1

Given data are

no. of observations n = 101

= 56.743

= 57.228

Sxy =  SUM (Xi -`X)*(Yi -`Y) = 4435.9

Sxx = (Xi -`X) = 4539.3

Estimation of coefficients

slope coefficient b1 = Sxy/Sxx = 4435.9/4539.3 = 0.977

intercept = b0 = = 57.228 - 0.977*56.743 = 1.790

Measured Weight = 1.790 + 0.977x Self-Reported Weight

The self reported is always less than the measured weight by 1.790 pounds. And also we can say that for every one additional unit increase in self reported weight the meaured weight increases by 0.977 units.