Practice of Statistics in the Life Sciences
Practice of Statistics in the Life Sciences
4th Edition
ISBN: 9781319013370
Author: Brigitte Baldi, David S. Moore
Publisher: W. H. Freeman
Question
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Chapter 23, Problem 23.34E

(a)

To determine

To find:

Theequation of the least-squares line of the given data.

(a)

Expert Solution
Check Mark

Answer to Problem 23.34E

  Y=31.93430.304X

Explanation of Solution

Given:

The previous year’s adult birds return =60%

Concept used:

Formula

The binomial distribution

  p[X=x]=(nx)pxqnx

Calculation:

The independent variable is X

The dependent variable is Y .

The regression coefficients,

Draw the table

    XYXYX2Y2
    745370547625
    666396435636
    818648656164
    52115722704121
    73128765329144
    62159303844225
    52168322704256
    45177652025289
    621811163844324
    46188282116324
    601911403600361
    46209202116400
    38207601444400
    X=757Y=185XY=10153X2=46119Y2=2969

  757 Xi= X = n y 58.230769230769 Σ Y = 185 = 14.230769230769 13 ssxx = Σ x21 Σ xi ) 461197572/13 ssxx= 2038.3076923077 ssY=Σ Y

Therefore, the regression coefficients (the slope m, and the y- intercept n).

The regression equation is

  Y=31.93430.304X

(b)

To determine

To find:

The equation of the least-squares line of the given data.

(b)

Expert Solution
Check Mark

Answer to Problem 23.34E

  Y31.93430.304 * 60 13.6943

Explanation of Solution

Given:

The previous year’s adult birds return =60%

Concept used:

Formula

The binomial distribution

  p[X=x]=(nx)pxqnx

Calculation:

The independent variable is X

The dependent variable is Y .

The regression coefficients,

Draw the table

    XYXYX2Y2
    745370547625
    666396435636
    818648656164
    52115722704121
    73128765329144
    62159303844225
    52168322704256
    45177652025289
    621811163844324
    46188282116324
    601911403600361
    46209202116400
    38207601444400
    X=757Y=185XY=10153X2=46119Y2=2969

  757 Xi= X = n y 58.230769230769 Σ Y = 185 = 14.230769230769 13 ssxx = Σ x21 Σ xi ) 461197572/13 ssxx= 2038.3076923077 ssY=Σ Y

Therefore, the regression coefficients (the slope m, and the y- intercept n).

The regression equation is

  Y=31.93430.304X

The slope of the regression line is

  m=0.304

Since the sign is negative,

Therefore the slope is a negative linear relationship between the percent return and new adults.

Also for every 1 percent increase of adult birds in a colony that return from the previous year, number of new adults that join the colony decreases by a factor of 0.304

By using X=60

  Y31.93430.304 * 60 13.6943

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