Question

Use the following linear regression equation to answer the questions.

x₃ = −17.3 + 3.7x₁ + 9.6x₄ − 1.7x₇

(e) Suppose that n = 20 data points were used to construct the given regression equation and that the standard error for the coefficient of x₄ is 0.820. Construct a 90% confidence interval for the coefficient of x₄. (Round your answers to two decimal places.)

lower limit
upper limit

(f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x₄ is different from zero. (Round your answers to two decimal places.)

t

=

t critical

= ±

Answer 1

(e) Let the co-efficient of x4 be b4.

Now, ~ t-distribution with (n-4) d.f.

Thus, 90% confidence interval of co-efficient of x4 is:

[, ], where, = 9.6,

s.e.() = 0.82, n = 20, = 1.746

= [8.1683, 11.0317].

Thus, lower limit = 8.1683 and upper limit = 11.0317. (Ans).

(f) The test-statistic for testing,H0: b4 = 0 against H1: b4 0

is, T = = 11.7073. (Ans).

The critical value = = 2.12. (Ans).

Since, observed test-statistic > critical value,

we reject H0 and conclude that the co-efficient of x4 is

significantly different from 0. (Ans).