Accounting-STA302 questions

STA302 questions

1. Fit a straight line to the data point and produce a plot of the data with the line of best fit superimposed.
( 20 Marks)
2. Give the least squares estimates ˆ 0 and ˆ 1 for the intercept 0 and and slope 1 in a simple linear
regression model. Repport also the least-squares equation arising from a least squares fit. ( 30 Marks)
3. Give an estimate of the variance 2. ( 5 Marks)
4. At level 5%, test H0 : 1 = 0 versus Ha : 1 6= 0. What is the pvalue of your test ? ( 20 Marks)
5. Use the least-squares equation to estimate the mean E(Y |X = 2.5) . Find a 95% confidence interval for
E(Y |X = 2.5). Is 0 a feasible value for E(Y |X = 2.5). Give a reason to support your answer. ( 15
Marks)
6. Find a 95% prediction interval for y at x=2.5. ( 10 Marks)
Extra Credit Questions: The adequacy of model
1. plot( against the x values) the residuals ei, i = 1, . . . , n, from the fit;
2. Comment on the adequcy of the straight line model, based on the residual plot that is, comment on
wether the assumption of the least squares fitted and how they relate to the residual errors ei are met
by the observed data.
Note : Below you have the R code to read the data set
# Read in data set
file1<-“Ass1.txt”
data1<-read.table(file1,header=TRUE)
plot(data1$x,data1$y,pch=18)
x1<-data1$x
y<-data1$y