Alternative approach to multiple regression analysis

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 R2, 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

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Observation: If k = 1, then

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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 H0: R = 0 (see Figure 1).

Regression F-test Excel

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.

6 thoughts on “Alternative approach to multiple regression analysis”

  1. 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

    Reply
    • 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

      Reply
    • 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

      Reply

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