My last linear regression post i mentioned that most of the numbers come form the residual errors, thats not entirely true. You have a basic understanding of lm you learned that R-square is the number to look at, that is based on residual error. You are also told to examine the p-value for each coefficient and for the entire model. P-value is a little bit harder to calculate, go search and find out for yourself. But in lieu of that i am going to provide the actual calculation for everything you may have seen reference in an lm.
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N,n: Upper case N is population size, lower case n is the sample size. <\/p>\n
Degrees of Freedom: Short uncomplicated, answer is the number of cases(rows) minus the number of coefficients. <\/p>\n
Mean: Average of a variable or column <\/p>\n
Variance: (sum(mean mpg – mpg) \/ n-1) <\/p>\n
Standard Deviation: sqrt(variance)<\/p>\n
Residuals: mpg – (slope + intercept * weight) <\/p>\n
Error Squared: Residuals^2<\/p>\n
Residual Standard Error RSE: variance \/ degrees of freedom <\/p>\n
SSE or Sum of Squared Errors: Sum(Error Squared)<\/p>\n
Multiple R-Squared: 1-SSE\/(sum(mpg – mean(mpg))^2)<\/p>\n
Adjusted R-Squared: 1-SSE\/(sum(mpg – mean(mpg))^2)*(n-1)\/(n-(1+1))<\/p>\n
Even i think this is ridiculous in a blog post, so i have included the excel spread sheet<\/a> on my github site if you really want to know how all of this works. IF everything goes well these numbers will match what came out of the R summary of lm for mtcars with mpg as the predictor and weight as the explanatory variable. <\/p>\n
![\"\"](\"https:\/\/sqlshep.com\/wp-content\/uploads\/2017\/12\/Screen-Shot-2017-12-20-at-5.19.37-PM.png\")
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