data: GPA ACT 3.897 21 3.885 14 3.778 28 2.540 22 3.028 21 3.865 31 2.962 32 3.9
ID: 3276842 • Letter: D
Question
data:
GPA ACT 3.897 21 3.885 14 3.778 28 2.540 22 3.028 21 3.865 31 2.962 32 3.961 27 0.500 29 3.178 26 3.310 24 3.538 30 3.083 24 3.013 24 3.245 33 2.963 27 3.522 25 3.013 31 2.947 25 2.118 20 2.563 24 3.357 21 3.731 28 3.925 27 3.556 28 3.101 26 2.420 28 2.579 22 3.871 26 3.060 21 3.927 25 2.375 16 2.929 28 3.375 26 2.857 22 3.072 24 3.381 21 3.290 30 3.549 27 3.646 26 2.978 26 2.654 30 2.540 24 2.250 26 2.069 29 2.617 24 2.183 31 2.000 15 2.952 19 3.806 18 2.871 27 3.352 16 3.305 27 2.952 26 3.547 24 3.691 30 3.160 21 2.194 20 3.323 30 3.936 29 2.922 25 2.716 23 3.370 25 3.606 23 2.642 30 2.452 21 2.655 24 3.714 32 1.806 18 3.516 23 3.039 20 2.966 23 2.482 18 2.700 18 3.920 29 2.834 20 3.222 23 3.084 26 4.000 28 3.511 34 3.323 20 3.072 20 2.079 26 3.875 32 3.208 25 2.920 27 3.345 27 3.956 29 3.808 19 2.506 21 3.886 24 2.183 27 3.429 25 3.024 18 3.750 29 3.833 24 3.113 27 2.875 21 2.747 19 2.311 18 1.841 25 1.583 18 2.879 20 3.591 32 2.914 24 3.716 35 2.800 25 3.621 28 3.792 28 2.867 25 3.419 22 3.600 30 2.394 20 2.286 20 1.486 31 3.885 20 3.800 29 3.914 28 1.860 16 2.948 28 Grade point average. The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X). The results of the study follow. Assume that first-order regression model (1.1) is appropriate. 18 119 120 28 i: 2 16 X 21 Y: 3.897 3.885 3.778... 14 28 3.9141.8602.948Explanation / Answer
I am using R software to solve this problem.
First we can copy the data into a .txt file and then import it into R using read.table() function.
Data <- read.table("Data.txt",sep=" ",header = T)
A linear model can be created in R using the lm() function as below.
model <- lm(GPA ~ ACT, data = Data)
a) Prediction can be done using the predict() function in R as below:
predict(model, data.frame(ACT=28), interval ="confidence", level = 0.95)
fit lwr upr
3.201209 3.061384 3.341033
We can say that we are 95% confident that the GPA score will lie between 3.061384 to 3.341033.
b) We can obtain the prediction interval as below:
predict(model, data.frame(ACT=28), interval ="prediction", level = 0.95)
fit lwr upr
3.201209 1.959355 4.443063
We can say that there is 95% probability that the GPA score of Mary Jones will be contained within the prediction interval from 1.959355 to 4.443063.
c) Yes the prediction interval is wider. That is always the case because prediction intervals are conceerned with the individual observations in a population as well as parameter estimates.
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