Question

Exhibit 16-4
In a laboratory experiment, data were gathered on the life span (Y in months) of 33 rats, units of daily protein intake (X₁), and whether or not agent X₂ (a proposed life extending agent) was added to the rats diet (X₂ = 0 if agent X₂ was not added, and X₂ = 1 if agent was added.) From the results of the experiment, the following regression model was developed.



Also provided are SSR = 60 and SST = 180.

Refer to Exhibit 16-4. The p-value for testing the significance of the regression model is

Group of answer choices

less than 0.01

between 0.01 and 0.025

between 0.025 and 0.05

between 0.05 and 0.10

Answer 1

Solution:

Given

n = 33 observation

k = 2 independent variables

Sum of square of regression = SSR = 60

Sum of square of total = SST = 180

SST = SSR + SSE

SSE = SST - SSR

SSE = 180 - 60

Sum of square of error = SSE = 120

Test for overall significance

To test the hypothesis

.

Vs.

Test statistic

F = 7.5

Test statistic F = 7.5

P Value = 0.002284 from online P value calculator

P Value = 0.0023

P Value less than 0.01

Option A is correct