STATISTICS Course

Regression table/model

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The regression model is defined by our equation $Y = a + b X + residual$. We are introducing, like in the tests, two hypotheses

  • $H0: b = 0$
  • $H1: b \neq 0$, meaning that b is significantly increasing Y

We are looking for $b$. Once you did evaluate your regression model (explained later), you will print it using summary giving you something like this

# simple linear regression - example - result
summary(model)

Call:
  lm(formula = hp ~ cyl, data = v)

Residuals:
  Min     1Q Median     3Q    Max
-54.61 -25.99 -11.28  21.51 130.39

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  -51.054     24.982  -2.044   0.0499 *
cyl           31.958      3.884   8.229 3.48e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 38.62 on 30 degrees of freedom
Multiple R-squared:  0.693,	Adjusted R-squared:  0.6827
F-statistic: 67.71 on 1 and 30 DF,  p-value: 3.478e-09

As you should have remembered

  • a: intercept coefficient and $a$ value is at the line "(Intercept)", column "Estimate".
  • b: our variable X is cyl so $b$ value is at the line "(cyl)", column "Estimate".
  • p-value : column Pr, as for the tests, it's indicating whether H0 or H1 may be the best fitting hypothesis.

You should read interpret the result as "if X is increasing by 1 then in average, Y tend to increase by $b$". Of course, you should check the p-value because the variable may not be correlated.

Note: You can easily get the correlation with $r = b * \frac{\sigma_{X}}{\sigma_{Y}}$.