Marmots are large, stocky animals. Yellow-bellied marmots are easily identified

Question

Marmots are large, stocky animals. Yellow-bellied marmots are easily identified by the brownish fur on their back coupled with their yellow to orange undersides. Males are larger than females. They usually weigh about ten pounds, and grow to about 30 inches. The mean length of 50 male marmots was found to be 10.74 inches with a standard deviation of 6.44 inches. The mean weight was found to be 7.7 pounds with a standard deviation of 2.64 pounds.

(a) Consider the scatterplot of length vs. weight. Describe the relationship between length and weight.

(b) 65.11% of the variation in length is explained by the least-squares regression line on weight. Find the correlation, r, between length and weight.

(c) Determine the least-squares linear regression line of length vs. weight.

(d) Interpret the slope

(e) Interpret the intercept, is it meaningful?

(f) Use your regression equation to predict the length of a marmot that weighs 10 pounds.

Explanation / Answer

a)

scatter-plot is not given

b)

r = sqrt(0.6511) = 0.80690

c)

lenght ^ = a + b * weight

y^ = a + b *x

b = cov(x,y) /var(X)

= r *sd (X) * sd(Y) /(var(X))

= r * sd(Y)/sd(X)

= 0.80690 * 6.44/2.64 = 1.9683469

a = ybar - b * xbar

= 10.74 - 1.9683469 * 7.7 = -4.416271

hence

y^ = -4.416271 +1.9683469   *x

length^ = -4.416271 +1.9683469   *weight

d) when the weight increase by 1 pound , on average the length increase by 1.9683469 inch

e)

length of marmots when weight = 0 is -4.416

no , it is not meaningful

f)

when weight = 10

length^ = -4.416271 +1.9683469   *10

= 15.267198 inch

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