Question

A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination? 

          A linear regression model based on a random sample of 36
observations on the response variable and 4 predictors has a
multiple coefficient of determination equal to 0.697. What is the
value of the adjusted multiple coefficient of determination?
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Added by Angela S.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?
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A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination? Answer:

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Transcript

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00:01 So let's look at the formula for adjusted r squared.
00:11 That is given by 1 minus, 1 minus the multiple coefficient of determination into, so we have n minus 1 divided by n minus k minus 1.
00:32 So here k is the number of predictors and is the sample size.
00:37 Okay so let's try this substitution here so we have one minus one minus now r squared has been given it a question to be 0 .697 times sample size is 36 minus 1 there we have 306 k is the number of predictors that is 4 minus 1 so we're going to have 1 minus 1 minus 1 1 minus 1 minus 1 697 here we're going to have 35 divided by 31 now let's see what we have here so we need to very careful with the algebra here so we're going to have one minus let's take off what is in the bracket so that's 1 minus 0 .697 we're going to have 0 .303 times 35 divided by 31...
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