The following model was fitted to a sample of 30 families in order to explain household milk consumption:
y = β0 + β1x1 + β2x2 + ε
where
y = milk consumption, in quarts per week
x1 = weekly income, in hundreds of dollars
x2 = family size
The least squares estimates of the regression parameters were as follows:
b0 = -0.025 b1 = 0.052 b2 = 1.14
The total sum of squares and regression sum of squares were found to be as follows:
SST = 162.1 and SSR = 88.2
A third independent variable—number of preschool children in the household—was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.7. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not linearly affect milk consumption.