Question

Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of aces burned for 7 recent years are shown.

Number of fires (x): 72 69 58 47 84 62 57

Number of acres burned (y): 73 70 59 48 85 63 58

The correlation coefficient for the data is r = 1 and standard deviation = 0.05.

Should the regression analysis be done?

Find the equation of the regression line. Round to three decimal places.

y' = ax+b

a =

b =

Answer 1

Here Dependent variable is Number of acres burned (y) and independent variable is Number of fires (x)

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As correlation between the two variables is 1.

But here point is that whether this correlation is meaningfull or nuinsance.So,this is a meaning ful correlation since logically we can estimate the Number of acres burned by using the number of fires in the forest.

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Question:-

Should the regression analysis be done?

Yes,Regression can be performed for the above data.

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Question:-

Find the equation of the regression line. Round to three decimal places.

y' = ax+b

a = Slope of the line

b = Intercept made by the line with the y-axis

Formulas to calculate a and b

Where xbar and ybar are the arithmetic means of x and y respectively.

Calculations:-(Model fitting)

(Excel is being used here)

cov(x,y) = 144.4672 ---- =covariance.s(array1,array2)

var(x) = 144.4672 ---- = var.s(number1,..number m)

Hence a= 144.4672 / 144.4672  

a = 1

And to calculate b;

xbar = 64.14286 ----=average(number1,...,number m )

ybar = 65.14286

b = 65.14286 - 1* 64.14286

b = 1

Therefore,

The regression line for the above data is

i.e

which is obvious since correlation(y,x) = 1