2. (35%) The following data were obtained from the U.S. Department of Interior,

Question

2. (35%) The following data were obtained from the U.S. Department of Interior, National Biological Service. Let x be the fall caribou population (in hundreds) in Denali National Park, and let y be the late winter wolf population in the park. Following is the data obtained from a random sample of recent years: Caribou(x) Wolfi66 30 34 79 27 70 2517 60 23 20 60 48 The sample correlation between x and y is r 915 for the n - 7 data points Summary Statistics Mean 25 63 Standard Deviation 6 10 Caribou(x) Wolfly) a. Do the data indicate a linear relationship between x and y? b. Predict the wolf population when the caribou population is x 30 using concept of regression toward mean. c. Predict the wolf population in (b) using the regression line itself. d. What percent of the variation in the data is explained by the regression line?

Explanation / Answer

SolutionA:

YES

correlation coefficient=

r=0.915

There exists a strong positive relationship between caribou and wolf

Solutionc

Obtain regression in excel

data>data analysis >regression

select data range

you get below o/p

y=22.36056+1.599296*x

for x=30 we have

y=22.36056+1.599296*30

y=70.33

y=70

rounding to nearest integer

ANSWER:70

Solutond:

R sq=0.8373

83.73% variation in y is explained by x.

Good model.

SUMMARY OUTPUT Regression Statistics Multiple R 0.915015 R Square 0.837252 Adjusted R Square 0.804703 Standard Error 4.491259 Observations 7 ANOVA df SS MS F Significance F Regression 1 518.8572 518.8572 25.72241 0.003861 Residual 5 100.857 20.17141 Total 6 619.7143 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 22.36056 8.108128 2.757796 0.039939 1.517956 43.20317 x 1.599296 0.315336 5.071727 0.003861 0.7887 2.409892

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