Question

Assume that you are building a regression model of the form

y = beta0 + beta1 x1 + beta2 x2 + beta3 x3 + E

where E is the random error term which is assumed to be normally distributed with mean 0 and constant variance.

Data from 16 subjects are collected for the purpose of this study. The R-Square value from the model is 0.60 and the total sums of squares variation is 1000. What is the p-value of the Global Test of Model Significance? Put your answer in 4 decimal places.

A regression model of the form y = beta0 + beta1 x1 + beta2 x2 + beta3 x3 + beta4 x4 + beta5 x5 + beta6 x6 + beta7 x7 + E is estimated. Here, E is assumed to be normally distributed with mean 0 and constant variance. You have been told that the R-Square value is 0.70, and that the Adj-R Square value is 0.60. What is the sample size?

Select one:

a. 29

b. 100

c. 19

d. Cannot be determined with the information given

e. 32

Answer 1

First Solution:

Given in question:

n=16

R2 = 0.60

R = 0.60 = 0.77

using calculator:

p- value is = 0.0004.

Second Solution:

Use adjusted R2 Formula to calculate the sample size:

n-is sample size.

k-is number of predictor in model exclude the intercept.

Given in question:

R2  = 0.70 and Adjusted R2 = 0.60

put in formula to calculate the sample size.

(0.30) (n-1) = 0.40 (n-8)

0.30n - 0.30 = 0.40n - 3.2

0.40n - 0.30n = 3.2 - 0.30

0.1n = 2.9

n = 2.9 / 0.1

n = 2.9*10

n = 29

So Answere is (a). 29.