Question

Given are five observations for two variables, x and y.

x i	1	2	3	4	5
y i	4	8	6	11	14

Round your answers to two decimal places.

a. Using the following equation:

Estimate the standard deviation of ŷ* when x = 4.

b. Using the following expression:

Develop a 95% confidence interval for the expected value of y when x = 4.

____to____

c. Using the following equation:

Estimate the standard deviation of an individual value of y when x = 4.

d. Using the following expression:

Develop a 95% prediction interval for y when x = 4. If your answer is negative, enter minus (-) sign.

____ to____

Answer 1

x<- c(1,2,3,4,5)
y <- c(4,8,6,11,14)

model <- lm(y ~ x)
summary(model)
predict(model,data.frame(x=4),interval="confidence",level=0.95)
predict(model,data.frame(x=4),interval="prediction",level=0.95)

a)
y^ = 1.7 + 2.3 *x

sd of y^ when x = 4

is 1.0149

b)

95% CI = (7.67,14.13)

c)

for PI, sd = 2.211661

d)
95 % PI = (4.18,17.62)