Question

3. R programming

3. This problem uses the wblake data set in the alr4 package. This data set includes samples of small mouth bass collected in West Bearskin Lake, Minnesota, in 1991 Interest is in predicting length with age. Complete this problem without using Im( in R (a) Do the regression of length on age, and report the estimates, their standard errors and the estimate of variance. Interpret Bo and (b) Obtain a 900% confidence interval for βί fron the data. Interpret this interval. (c) Obtain a prediction and a 90% prediction interval for a small mouth bass at age 2. Interpret this interval

Answer 1

a).

library(alr4)
data(wblake)
head(wblake)
To fit this model,

Our response varaible (y) is "Length" and predictor variable (x) is "Age"

M1=lm(Length~1+Age,data=wblake)
summary(M1)

Output:

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 65.5272 3.1974 20.49 <2e-16 ***
Age 30.3239 0.6877 44.09 <2e-16 ***

65.5272. 31=30.3239

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b).

90% confidence interval for slope (i.e. ) is

61

  

$t^*$ is the critical t value for n-2 degree of freedom.

Degree od freedom = n-2 = 439-2 = 437 (Total no. of observation in wblake data is 439)

Therefore, critical t value at () for 437 degree of freedom is calculated in R as:

qt(1-0.10/2,437)

1.65

From (1), we have

31 ± t*se(31)

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