The ?nal test and exam averages for 20 randomly selected students taking a cours
ID: 3155219 • Letter: T
Question
The ?nal test and exam averages for 20 randomly selected students taking a course in en-gineering statistics and a course in operations research are as follow. Assume that the ?nal
averages are jointly normally distributed. The R outputs of the linear regression procedure are as follows:
(a) Find the regression line relating the statistics ?nal average to the OR ?nal average.
(b) Base on the regression model, what is the OR ?nal average given that the statistics ?nal average is 84? What is the residual?
(c) Predict the OR ?nal average when statistics ?nal average is 80.
(d) Test the hypotheses H0 : ?1 = 0 versus H1 : ?1 6= 0.
(e) What is an estimate of ?2?
(f) What is the coe?cient of determination, R2?
Sorry for the length but could someone please help! Please answer ALL questions with good detail. THANK YOU.
Explanation / Answer
(a)
independent variable (X) : The statistics final average
dependent variable (X) : The OR final average
The required linear regression equation is
y' = 0.82344x + 14.75967
(b)
For X= 84 the predicted OR final average is
y' = 0.82344*84 + 14.75967 = 83.92863
Observed value for X = 84 is 85.
So residual : observed value - predicted value = 85 - 83.92863 = 1.07137
(c)
For X= 80 the predicted OR final average is
y' = 0.82344*80 + 14.75967 = 80.63487
(d)
Here we need p-value corresponding to the slope.
From the output the p-value of the t test is 0.0000 (for one tailed test) so for two tailed test it will be 0.0000. Since p-value is less than 0.01 so slope is siginificant to the model.
(e)
An estimate of 2 is 3.913
(f)
the coecient of determination, R2 is 0.816
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