least squares regression line - Danila breeds peregrine falcons. She recorded the breadth (in mm) of each egg and the mass (in g) of the falcon chick that hatched from it. After plotting her results, Danila noticed that the relationship between the two variables was fairly linear. This is computer output from a least-squares regression analysis on the data: Predictor Coef SE Coef T P Constant -266.53 51.03 -5.22 0.001 Breadth (mm) 6.1376 0;7353 8.35 0.000 S = 8.641 R-Sq = 89.7% R-Sq (adj) = 88.4% What is the equation of the least-squares line and what is the residual of a 39 g falcon chick who hatches from an egg with a breadth of 35 mm?

Danila breeds peregrine falcons. She recorded the breadth (in mm) of each egg and the mass (in g) of the falcon chick that hatched from it. After plotting her results, Danila noticed that the relationship between the two variables was fairly linear. This is computer output from a least-squares regression analysis on the data: Predictor Coef SE Coef T P Constant -266.53 51.03 -5.22 0.001 Breadth (mm) 6.1376 0;7353 8.35 0.000 S = 8.641 R-Sq = 89.7% R-Sq (adj) = 88.4% What is the equation of the least-squares line and what is the residual of a 39 g falcon chick who hatches from an egg with a breadth of 35 mm?

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Sahil Khan (last edited 2 years ago)

This is the computer regression output given.

Breadth (mm) is the explanatory (x) variable in this situation and mass (g) is the response (y) variable.

We need the slope and the y-intercept to write the equation of the regression line in the form \widehat{y}=a+bx

The constant coefficient -266.53 is the y-intercept and the breadth coefficient 6.1376 is the slope

So, the equation of the least-squares line is \widehat{y} = 6.14 x -266.53.

Now, plug in x = 35 mm, in this to get \widehat{y} = 6.14 \cdot 35 - 266.53 = -51.63 g.

The residual is the difference between the observed value y and the predicted value \widehat{y}.

Residual = 39 g - 51.63 g = -12.63 g.

So, the residual of a 39 g falcon chick who hatches from an egg with a breadth of 35 mm is -12.63 grams.

Qalaxia Knowlege Bot (last edited 2 years ago)

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I found an answer from downloads.cs.stanford.edu

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Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

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