The table below gives the height and weight of four randomly selected University undergraduate women. What is the least squares error E for these data points? $\begin{array} { r r r r r }
\text { height } ( \mathrm { cm } ) & 150 & 155 & 165 & 170 \
\hline \text { weight } ( \mathrm { kg } ) & 60 & 55 & 70 & 62
\end{array}$
A) E = (150A + 60B $)^2$ + (155A + 55B $)^2$ + (165A + 70B $)^2$ + (170A + 62B $)^2$
B) E = 150(A + B - 60 $)^2$ + 155(A + B - 55 $)^2$ + 165(A + B - 70 $)^2$ + 170(A + B - 62 $)^2$
C) E = (150A - 60B $)^2$ + (155A - 55B $)^2$ + (165A - 70B $)^2$ + (170A - 62B $)^2$
D) E = (150A + B - 60 $)^2$ + (155A + B - 55 $)^2$ + (165A + B - 70 $)^2$ + (170A + B - 62 $)^2$
E) none of these

Question

The table below gives the height and weight of four randomly selected University undergraduate women. What is the least squares error E for these data points? $\begin{array} { r r r r r } 
\text { height } ( \mathrm { cm } ) & 150 & 155 & 165 & 170 \
\hline \text { weight } ( \mathrm { kg } ) & 60 & 55 & 70 & 62
\end{array}$
A) E = (150A + 60B $)^2$ + (155A + 55B $)^2$ + (165A + 70B $)^2$ + (170A + 62B $)^2$
B) E = 150(A + B - 60 $)^2$ + 155(A + B - 55 $)^2$ + 165(A + B - 70 $)^2$ + 170(A + B - 62 $)^2$
C) E = (150A - 60B $)^2$ + (155A - 55B $)^2$ + (165A - 70B $)^2$ + (170A - 62B $)^2$
D) E = (150A + B - 60 $)^2$ + (155A + B - 55 $)^2$ + (165A + B - 70 $)^2$ + (170A + B - 62 $)^2$
E) none of these

Quizplus · Accepted Answer

The least squares error formula for a linear regression model (y = Ax + B) involves the sum of the squares of the differences between the observed values (y) and the values predicted by the model (Ax + B). The correct formula is given by option D, where for each data point, the squared difference between the actual weight (y) and the predicted weight (Ax + B) is calculated and summed up.

The Table Below Gives the Height and Weight of Four