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A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown.
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm .

A random sample of 65 high school seniors was selected from all high school seniors at a certain high school The following scatterplot shows the height in centi class=
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school The following scatterplot shows the height in centi class=

Respuesta :

MathPhys

Step-by-step explanation:

The line of best fit is y = 2.599x + 105.08.  At x = 20, the estimated height is y = 157.06.  The actual height is 160 cm, so the residual is:

160 cm − 157.06 cm = 2.94 cm

Cricetus

The residual for the high school senior will be "2.94 cm".

According to the question,

At foot length,

  • 20 cm

Height,

  • 160 cm

The regression equation is:

→ [tex]Height = 105.08+2.599\times foot \ length[/tex]

By substituting the value, we get

→             [tex]= 105.08+2.599\times 20[/tex]

→             [tex]= 157.06 \ cm[/tex]

hence,

→ [tex]Residual = Actual-Predicted \ value[/tex]

→                [tex]= 160-157.06[/tex]

→                [tex]=2.94 \ cm[/tex]

Thus the answer above is correct.  

Learn more:

https://brainly.com/question/18818087

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