The data set for the average height of men at a ballgame compared to their shoe size is represented by the table.

Question

Part A: What is the equation of the least-squares regression line?

Part B: Carlos wears a size 9 and is 71 inches tall. What is the residual for Carlos's data? Show your work.

Part C: Interpret the meaning of the residual from part B.

Answer 1

Robin

If you have a TI-84 enter the shoe size values in List 1, and the heights in List 2.

Then STAT CALC 4

X List = L1, Y List = L5, Freq list empty Calculate

a = 1.313

b = 56.143

So the model is height = 1.313 x shoe size + 56.143

r = 0.837 so we have a strong linear relationship between height and shoe size

Residual = observed - predicted

for size 9, predicted = 1.313 x 9 + 56.143 = 67.96

observed = 71

residual = 71 - 67.96 = 3.04

As the residual is positive, this tells us that Carlos is above average height for his shoe size.