Another way of determining whether a regression model is a good fit is to look at whether the population multiple correlation coefficient *R* between y and ŷ is zero (the null hypothesis). As noted in Multiple Correlation a sample’s adjusted *R* is an unbiased estimate of the population *R*. Instead of *R*, we generally test *R ^{2}*, and use the following property, which is an extension of Theorem 1 of One Sample Testing of Correlation.

**Property 1**: If the population *R* = 0, then

**Observation**: If *k* = 1, then

is equivalent to Theorem 1 of One Sample Testing of Correlation (by Property 1 of F Distribution).

**Example 1**: Show that the regression model in Example 2 of Multiple Regression Analysis is a good fit by using Property 1.

We test the null hypothesis H_{0}: *R* = 0 (see Figure 1).

**Figure 1 – F****-test of data in ****Example 1 using Property 1**

As we can see from the above analysis, we reject the null hypothesis, and conclude that the fit of the regression model with the data is not due simply to chance.

hi,

we have data set regarding the cpu,s and attributes are like clock speed ,memory,cache and performance and we like to predict how performance depend on the memory,clock speed,cache attributes using linear regression or non linear regression and estimate the performances if other attributes are given

can u help which method will be better and how to approach it

Hello,

This really depends on a number of factors, most importantly (1) any theoretical or domain-related reasons for preferring one over the other and (2) the nature of the data. Without more information, I am unable to comment further.

Charles

Your articles are wonderful.

sir

Is there any test – to test the coefficients b1,b2,…bk in the multiple regression model for fit their population coefficients

Grandhi,

The usual test is t = (bi-βi)/se ~ T(n-k-1) where βi is the known or hypothesized population coefficient, n = the sample size, k = # of parameters and se is the standard error for bi.

Charles

what does it mean, the df,ss,ms,f,and significance f?

Sorry, but i don’t see these symbols on the referenced webpage. You can find the definitions of these symbols on the webpage

Multiple Regression Analysis in Excel.

Charles