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Secure https:/Ing.cengage.com/static/nb/jui/evojindex htm/?elSBN-97813055864378nb Lora." D Requisite Fitness-- 11 Learning on Simpil.. ? Association for Co- O on AP Use computer software packages, such as Minitab or Excel, to solve this problem. Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 29 47 25 51 40 52 75 37 59 76 X2 13 95 109 112 179 95 175 18 17 19 13 13 17 118 142 211 The estimated regression equation for this data is 9-18.5+ 2.03x1 + 4.48x2 Round your answers to two decimal places. a. Develop a 95% confidence interval for the mean value of y when X1 95% confidence interval is 45 and X2-15. to 45 and x2 = 15. b. Develop a 95% prediction interval for y when X1, to 95% prediction interval is 81761

Explanation / Answer

SolutionA:

used R software.

lm used lm to build a regression model

x1 <- c(29,47,25,51,40,52,75,37,59,76)
x2 <- c(13,11,18,17,5,19,7,13,13,17)
y <- c(95,109,112,179,95,175,171,118,142,211)
mod.lm=lm(y~x1+x2)
coefficients(mod.lm)

newdata = data.frame(x1=45,x2=15)
predict(mod.lm, newdata, interval="confidence")

output:

fit lwr upr
1 139.9955 129.8277 150.1633

95% confidence interval is

129.83 to 150.16

Solutionb:

prediction interval is given by:

x1 <- c(29,47,25,51,40,52,75,37,59,76)
x2 <- c(13,11,18,17,5,19,7,13,13,17)
y <- c(95,109,112,179,95,175,171,118,142,211)
mod.lm=lm(y~x1+x2)
coefficients(mod.lm)

newdata = data.frame(x1=45,x2=15)

predict(mod.lm, newdata, interval="predict")

Output:

fit lwr upr
1 139.9955 108.8556 171.1354

95% prediction interval is

108.86 to 171.14

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