Brittany rents bicycles to tourists. She recorded the height (in cm) of each customer and the frame size (in cm) of the bicycle that customer rented. After plotting her results, Brittany noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting bicycle frame size from the height of the customer: y=x+ What is the residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame?

-1

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Brittany rents bicycles to tourists. She recorded the height (in cm) of each customer and the frame size (in cm) of the bicycle that customer rented. After plotting her results, Brittany noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting bicycle frame size from the height of the customer: y'=1/3x + 1/3.

What is the residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame?

The regression equation is given as:

y'=(1/3)x + (1/3)

Since the height is given as 155cm, x=155 cm

The predicted frame size,

y'=(1/3)x + (1/3)

y'=(1/3) × 155+ (1/3)

= 51 2/3 + 1/3

= 52

The observed frame size,

y=51

Residual = Observed y- predicted y

=51-52

= -1

The residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame is -1.

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