Listed below are the numbers of forest fires (in thousands) and the acres that were burned...

Listed below are the numbers of forest fires (in thousands) and the acres that were burned (in
hundred thousands) during a year.

Fires, x	72	69	58	47	84	62	57	45
Acres, y	62	41	19	26	51	15	30	15

a) Find the value of the linear correlation coefficient r and use a significance level of α = 0.05 to
determine whether there is a significant linear correlation between the two variables.

b) Find the best predicted value for the number of acres burned given that there were 60
thousand fires.

Expert Solution

Run a regression analysis in excel followed by below procedures:

1. Go to data tab --> data analysis --> choose Regression

Correlation coefficient r = 0.769

Significance F (P-value) = 0.03

P-value is lesser than the significance level 0.05

If the p-value is less than the significance level (α=0.05):

Decision: Reject the null hypothesis.
Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero."

orchestra answered 2 years ago

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