Question

The computer output given below shows a regression of Body Mass (g) vs. Wing Length (mm) for sphinx moths.

Regression Analysis
Body Mass = −1.211 + 0.057 Wing Length

Summary of Fit
RSquare	0.694
RSquare Adj	0.682
S	0.513

Analysis of Variance
Source	DF	SS	MS	F	P-value
Model	1	15.54	15.541	59.03	<.0001
Error	26	6.84	0.263
Total	27	22.39

Parameter Estimates
Term	Estimate	Std Error	t Ratio	Prob>|t|
Intercept	−1.2116	0.3424	−3.539	0.0015
Wing Length	0.0573	0.0072	7.9588	<.0001

i) Find the y-intercept.

a) What is the estimated regression line?

ii) Find the estimate of the slop parameter.

b) What is the calculated value of s_b?

c) What is the calculated value of s_e?

e) Assuming all necessary assumptions are satisfied, perform the Model Utility Test for this problem.

What is the value of the t-test statistic?

f) Construct a 95% confidence interval for β.

i) Find the lower bound.

f) Construct a 95% confidence interval for β.

ii) Find the upper bound.

Answer 1

(a): The estimated regression line is:

Body Mass = −1.211 + 0.057 Wing Length

i): The y-intercept is −1.211.

ii): The estimate of the slope parameter is 0.057.

(b): From the table, the calculated value of sb is 0.0072.

(c): From the table, the calculated value of se is given as: