Question

Suppose that a​ researcher, using data on 150 randomly selected​ bicycles, estimates the OLS​ regression: ModifyingAbove Price with caret equals 672.65 minus 1.56 times Weight​, ​(191.4​) ​(0.28​) where Price measures the price of the i Superscript th bike in dollars and Weight measures the weight of the i Superscript th bike in kilograms. The​ 99% confidence interval for the​ intercept, beta 0​, will be ​( nothing​, nothing​).

Answer 1

99% CI for the intercept (b₀) [173.29; 1172.01]dollars

Explanation:

Hello!

You have the information of two variables

Y: price of a bycicle (dollars)

X: Weight of a bycicle (kilograms)

The estimated regression equation is

^Y= 672.65 - 1.56X

(191.4) (0.28)

Assuming that 191.4 is the estimated standard deviation of the intercept and 0.28 corresponds to the estimated standard deviation of the slope. The statistic you can use to estimate the intercept is a student's t.

99% CI for the intercept (b₀):

b₀ ± tₙ₋₂;1-α * Sb₀

tₙ₋₂;1-α= t₁₄₈;₀.₉₉₅= 2.609

672.65 ± (2.609*191.4)

[173.2874; 1172.0126]dollars

I hope it helps!