MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Data SetGeese

Sample

Variables = 3

Observations = 45

Variables>Observations>

Variable

Correlation

Count from a Photo and Observers' Estimates of the Size of Flocks of Geese

Name: Experienced observers use aerial survey methods to estimate the number
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Experienced observers use aerial survey methods to estimate the number of snow geese in their summer range area west of Hudson Bay, Canada. A small aircraft flies over the range, and when a flock of geese is spotted, the observer estimates the number

C. E. Lunneborg, Modeling Experimental and Observational Data, Duxbury Press, 1994

Variable↓	Type↓	Form↓	Observations
Values↓	Missing↓
Photo	Quantitative	Numeric	45	0
A Estimate	Quantitative	Numeric	45	0
B Estimate	Quantitative	Numeric	45	0

You will work with goose observer A’s estimates in this problem to examine how well observer A’s estimates predict counts from the associated photographs for the same flock. The photographs provide a highly accurate count of geese; optimally, the observer’s estimate would predict the photo-based count for a specific flock.

First, use the regression equation to predict Y values based on observer A’s estimates. The regression equation, in the format Ŷ = bX + a, is:

Ŷ = 0.88X + 26.65

where X = goose observer A’s estimate,

Ŷ = an estimate of the goose count from the photograph

In this problem, Y is the actual count of geese in the photograph.

Note: The estimated regression equation can also be obtained by going to the Correlation section in the DataView tool, specifying the proper dependent (Y) and independent (X) variables, and clicking on the Linear Regression button.

Find the predicted Y values for the flocks 2, 17, and 35. Ŷ for flock 2 is . Ŷ for flock 17 is . Ŷ for flock 35 is . You will need to use the Observations list in the DataView tool to identify goose observer A’s estimate for the appropriate flock. Click on the Observations button in the tool, and scroll to the appropriate flock number.

Calculate the residuals for the flocks identified. The residual for flock 2 is . The residual for flock 17 is . The residual for flock 35 is .

You want to test the significance of this regression equation. The null hypothesis can be phrased as:

The intercept of the regression equation is greater than zero.

The regression equation accounts for a significant portion of the variance in the y scores (counts from the photos).

The slope of the regression equation is greater than zero.

The regression equation does not account for a significant portion of the variance in the y scores (counts from the photos).

The Pearson correlation is r = 0.8662, SSXX = 327,086.00, and SSYY = 339,559.64. Calculate the predicted variability, the unpredicted variability, and the percentage of the variance explained by the regression equation mentioned previously. The predicted variability is . The unpredicted variability is . The percentage of the variance explained is .

Use the Distributions tool to help you test the null hypothesis.(Note: Do not use the F-table to calculate the critical value as the answer requires an of an exact df to calculate the value.)

F Distribution

Numerator Degrees of Freedom = 26

Denominator Degrees of Freedom = 26

0.001.002.003.004.005.006.007.008.00F

To test the null hypothesis, you will first need to find the critical value of F at alpha = 0.05. F is . Next, calculate the F-ratio. The F-ratio is . Therefore, the null hypothesis is . On the basis of these results, you conclude that the regression equation accounts for a significant portion of the variance in the y scores (counts from the photos).

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