Consider linear regression for a supervised learning problem...

Consider linear regression for a supervised learning problem with 15 features and a training dataset of size 50. We wish to test whether the features {x2, x4, x6, x14} are significant for predicting the output. In do- ing that we compute the appropriate F-ratio. Under which F-distribution are we to interpret the F-ratio?

Transcript

00:01 And then the regression analysis involving 30 observations, the following estimated regression equation was obtained.

00:08 For this estimated regression equation, the sum of squares total was 1805, the sum of squares residual 1760.

00:15 At alph's 0 .05 test the significance of the relationship among the variables.

00:20 So we want the f.

00:22 So the f is going to be the mean square residual over mean square error.

00:35 That's going to be the sum of squares residual over the number of independent variables.

00:42 So here, k is four independent variables, x1, x2, x, 3, x4.

00:47 And then the mean square errors, the sum of square errors over the number of observations n minus independent variables minus 1.

00:56 Okay, and note that sse is the total sum of squares minus the residual.

01:04 So here's 1805 minus 1760 and 45.

01:14 And n here is 30.

01:23 So the statistic is sum of squares residual 1760 over number of independent variables 4 divided by some square error 45 over 30 minus 4 minus 1.

01:40 So we can get out our calculator for this.

01:46 So we're going to have 1760 over 4, 5 by 45 over 25.

01:58 Okay, so the f statistic is 244 .44 for repeat.

02:08 Okay, so this f statistic here, okay, is an f with four degrees of freedom and 25 degrees of freedom.

02:18 So what we know then is that the p value is the probability, that x is more than this critical value to 44, or not critical value, the test statistic point four repeat.

02:35 And so i'm going to use r for this, that we want one minus the probability in the f distribution that were more than, well, this one minus probability were less than 244 .4 repeat on four and 25 degrees of freedom.

02:52 Okay, so probability is zero.

02:54 It's so, so small.

02:57 So it certainly is less than the critical 0 .05, so the model is significant...

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