A fisheries biologist has been studying horseshoe crabs She

A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is

where the deviations _i are assumed to be independent and Normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software:

(b) The quantity s = 2.2018 is an estimate of the standard deviation, , of the deviations in the simple linear regression model. The degrees of freedom for s are

a.) 100

b.) 99     

c.) 98

d.) 2

(c) The y-intercept of the least-squares regression line is

a.) 0.0939

b.) 0.7963   

c.) 0.9788

d.) 2.3013

(d) Suppose the researchers test the following hypotheses: H ₀ : ₁ = 0 versus H _a: ₁ > 0.
The value of the t statistic for this test is

a.) 0.36

b.) 2.35     

c.) 3.57

d.) 8.48

(e) A 95% confidence interval for the slope ₁ in the simple linear regression model is (approximately)

a.) 0.7963 ± 0.1863

b.) 2.3013 ± 1.9419     

c.) 2.3013 ± 0.1863

d.) 0.7963 ± 1.9419

Solution

b) The quantity s = 2.2018 is an estimate of the standard deviation, , of the deviations in the simple linear regression model. The degrees of freedom for s are 100-1=99

(c) The y-intercept of the least-squares regression line is  d.) 2.3013

d)The value of test statistic t is: b1/SE=0.7963/0.0939=8.48

(e)The 95% CI for slope is:

0.7963+/-t(99,0.95)*0.0939

=0.7963+/-1.984*0.0939

=0.7963+/-0.1863