Question

** Remember, there are examples in your notes at the end of each section**

The data set "cars" in R has 2 variables with 50 observations.
speed: numeric Speed (mph)
dist: numeric Stopping distance (ft)

Fill in the missing boxes below in the R code and then the corresponding predictor table from R.

Assume we want to test if dist a car travels can be determined by speed.

dat.lm = lm( __ ~ __ , data = __ )summary( __ )

	Estimate	Std. Error	t	Pr(>|t|)
Intercept				0.0123
speed				1.49e-12

a) Write the least squares line from the table above in the form ?̂= a + bx but filling the with the estimates of the coefficients.
?̂= __ + __x

b) Is there evidence to support that dist increases as the speed increases? Use ?=0.05.
1. ?₀ : ?₁ = 0 vs. ?? : ?₁> 0
2. ? = 0.05

3. t = __

4. Critical t_0.05,48 = t_0.05,40 = __

5. Conclusion:
Reject H0 OR Fail to reject H0

Interpretation:
There is sufficient evidence to support that dist increases as speed increases. OR
There is not sufficient evidence to support that dist increases as speed increases.

c) Find the 90% confidence interval for ?.

confint(dat.lm, 'speed', level = 0.90)

( __ , __ )

d) Find the 95% prediction interval for the mean when speed = 22.

newdat = data.frame( __ = __ )
predict( __ , __ , interval = 'prediction')

fit = __ , lwr = __ , upr = __

Answer 1

code :