# What does this linear regression summary tells us?

I just started learning predictive modelling in R , however i do understand some terms below but i lack in making more interpretations , just want to know what a pro statistician or Data Scientist interpret from it . How does one look at it ?

> summary(model)

Call:
lm(formula = comp$Minutes ~ comp$Units)

Residuals:
Min      1Q  Median      3Q     Max
-9.2318 -3.3415 -0.7143  4.7769  7.8033

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)    4.162      3.355    1.24    0.239
comp$Units 15.509 0.505 30.71 8.92e-13 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 5.392 on 12 degrees of freedom Multiple R-squared: 0.9874, Adjusted R-squared: 0.9864 F-statistic: 943.2 on 1 and 12 DF, p-value: 8.916e-13  • You can just type in R ?summary.lm. The documentation tells you the statistics name of each word, and you can then use wikipedia to learn more about each. – Ricardo Cruz Aug 1 '16 at 13:32 • Ah, this specific summary!$\beta_0=4.2$and$\beta_1=15.5$. Your$\beta_1$is statistically significative (t-test << 0.05).$R^2=0.99$meaning 0.99 of the variance in the dependent variable is explained by your regression. Finally, the F-test is statistically significative as well. In other words, it looks like a good regression. – Ricardo Cruz Aug 1 '16 at 14:37 • @RicardoCruz This'd make a good answer :) – Dawny33 Aug 4 '16 at 10:52 • From experience, not from theory,$R^2=.99 $is an unusually large result. Here is the point: the p-value is calculated under the assumption that the residuals follow a certain pattern, and without checking that you cannot trust the p-value. You have only 14 observations, so a few extreme outliers would easily invalidate the assumptions needed to compute the p-values. Plot the pairs (comp$Minutes, residuals) and check if there are a few large residuals. – VictorZurkowski Aug 5 '16 at 0:23
• What @VictorZurkowski said. I did not actually "answer" the question because it would involve mentioning all those things. Anyhow, here is a list of the typical assumptions when hypothesis-testing a linear regression. Since you only have one variable, you can plot the regression for that variable and see if the residuals (difference between your line and the points) make sense. The difference should be uniform across the variable. See here how to plot it. – Ricardo Cruz Aug 5 '16 at 10:45