Sometimes it is known from theoretical considerations that the straight-line relationship between two variables, x and y,
Question:
y = β1x + ε
The least squares estimate of β1 for this model is
From the records of past flour shipments, 15 shipments were randomly chosen, and the data shown in the table below were recorded.
a. Find the least squares line for the given data under the assumption that β0 = 0. Plot the least squares line on a scatter plot of the data.
b. Find the least squares line for the given data using the model
y = β0 + β1x + ε
(i.e., do not restrict β0 to equal 0). Plot this line on the same scatter plot you constructed in part a.
c. Refer to part b. Why might 0 be different from 0 even though the true value of β0 is known to be 0?
d. The estimated standard error of 0 is equal to
Use the t-statistic
to test the null hypothesis H0: β0 = 0 against the alternative Ha: β0 ‰ 0. Use α = .10. Should you include β0 in your model?
Step by Step Answer:
Statistics For Business And Economics
ISBN: 9780321826237
12th Edition
Authors: James T. McClave, P. George Benson, Terry T Sincich