Question

An independent researcher wants to investigate if the factors which determine the house rent (Y, measured in dollars), such as the distance of the house from the airport (X₁), the time since the house was built (X₂), are significant or not. He collects data from 120 prospective locations and estimates the following regression equation:

Ŷ_i = 2.5 – 1.23 X₁ + 0.98 X₂

                 (2.45)     (2.14)

Calculate the 95% confidence interval for the slope (Round your answer to two decimal places. Enter a minus sign if your answer is negative.).

Note: df = 117, alpha = 0.05, slope = -1.23, Standard Error = 2.45

Answer 1

Solution:

The required confidence interval for the slope is given as below:

Confidence interval = slope ± t*Standard error

We are given

Slope = -1.23

Standard error = 2.45

Confidence level = 95%

df = 117

Critical t value = 1.9804

(by using t-table or excel)

Confidence interval = slope ± t*Standard error

Confidence interval = -1.23 ± 1.9804*2.45

Confidence interval = -1.23 ± 4.85198

Lower limit = -1.23 - 4.85198 = -6.08198

Upper limit = -1.23 + 4.85198 = 3.62198

Confidence interval = (-6.08, 3.62)