Question

The accompanying data were read from graphs that appeared in an article. The variables shown are the number of acres burned in forest fires in the western United States and timber sales.

Year	Number of Acres Burned (thousands)	Timber Sales (billions of board feet)
1945	206	2.1
1950	258	3.7
1955	250	4.5
1960	388	6.7
1965	80	9.7
1970	460	11.2
1975	173	10.9
1980	242	10.2
1985	449	9.9
1990	403	10.9
1995	187	3.8

(a) Compute the correlation coefficient. (Give the answer to three decimal places.)
r =  
Is there a correlation between timber sales and acres burned in forest fires?

strong positive correlationweak positive correlation    strong negative correlationweak negative correlationno correlation

(b) The article concludes that "heavier logging led to large forest fires." Do you think this conclusion is justified based on the given data?

YesNo

Answer 1

x: Number of Acres Burned
y: Timber Sales

a) We have to find correlation coefficient r

Formula is

n = 11

	x	y	xy	x^2	y^2
	206	2.1	432.6	42436	4.41
	258	3.7	954.6	66564	13.69
	250	4.5	1125	62500	20.25
	388	6.7	2599.6	150544	44.89
	80	9.7	776	6400	94.09
	460	11.2	5152	211600	125.44
	173	10.9	1885.7	29929	118.81
	242	10.2	2468.4	58564	104.04
	449	9.9	4445.1	201601	98.01
	403	10.9	4392.7	162409	118.81
	187	3.8	710.6	34969	14.44
Total	3096	83.6	24942.3	1027516	756.88

There is a weak positive correlation between timber sales and acres burned in forest fires.

b)  

There is a weak positive correlation between timber sales and acres burned in forest fires.

So heavier logging led to large forest fires this statement is wrong.

No