# Statistical significance on intercept and slope

I am asked to do a regression analysis on distance ~ speed in R. Using the following code:

fit <- lm(dist ~ speed)
summary(fit)


I obtained:

            Estimate Std. Error t value Pr(>|t|)
(Intercept) -17.5791     6.7584  -2.601   0.0123 *
speed         3.9324     0.4155   9.464 1.49e-12 ***


I am asked:

Can we conclude that the slope is greater than zero? Can we conclude that the intercept is smaller than zero? Report the relevant p-values to support your conclusions.

I am not exactly sure what they ask me to do in this question. Can I draw the conclusions from information obtained by the summary-command or should I make a confidence interval? I would say the $p$-values in this case show that there is enough statistical significance to conclude that the intercept < 0 and speed > 0.

• if this is HW please add the self-study tag – Antoine Mar 1 '16 at 15:59
• I think you have the answers there. Just a couple of points on the R nomenclature: the intercept is spelled out, but the speed is the slope. Other than that, it seems like a homework problem that you can research. – Antoni Parellada Mar 1 '16 at 16:08