The coefficients summary table and ANOVA table from the full ANCOVA model are pr
ID: 3252872 • Letter: T
Question
The coefficients summary table and ANOVA table from the full ANCOVA model are presented below. Note that diesel-fuelled vehicles have been used as the reference group in this analysis.
(a) What values should go in the cells labelled (1) to (4) in the ANOVA table?
(b) Is the full ANCOVA model needed or could we plausibly use a parallel ANCOVA? (Don’t forget to justify your answer.)
( c) Find a 99% confidence interval for the difference between the slopes for petrolfuelled and diesel-fuelled vehicles in this model.
(d) Test whether there is a statistically significant difference between the intercepts for the two different fuel types in this model.
(e)Write down the fitted equation for the fuel economy of a petrol-fuelled 4WD vehicle according to this model.
f) The residual and normal probability plots for the full ANCOVA model are presented below. Based on these plots, are there any issues with the underlying assumptions of this ANCOVA model? [Note: as explained in Practical 10, a normal probability plot is interpreted similarly to the normal Q-Q plots discussed in lectures.]
18 16 14 o 12 10 Scatterplot of economy vs capacity 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 capacity fuel diesel petrolExplanation / Answer
Answer to part a)
MS = SS / df
So value of 1 = 78.486
Value of 2 is
MS = 43.201
SS = 43.201
MS = SS / df
So we get = 43.201 = 43.201 /df
Thus df = 1
Thus value of [2] is 1
similarly value of [3] is 1
.
value of [4]
1.653 = 19.832 / df
df = 19.832 / 1.653 = 11.99
Thus means value of [4] is 12
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Answer to part b)
We can plausibly use a Parallel ANOCVA for this situation
Parallel ANCOVA is used when there is no interaction in the independent variables , or in graphical terms they both have parallel lines. Full ANCOVA is used only where the interaction of the two independent variables is also signfiicant . In the given table we find that the P value of interaction is 0.254 , which implies that the interaction is not signifcant . And if the interaction is not significant then Parallel ANCOVA best suits this data.
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Answer to part c)
Slope difference - t. SE , Slope difference + t*SE
t critical = 3.055
.
Slope difference = 1.30
SE = 1.08
.
On plugging the values we get:
1.30 - 3.055 *1.08 , 1.30 + 3.055*1.08
-1.9994 , 4.5994
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Answer to part d)
Since the P value for constant difference is 0.726
it is very large
this means there is no signficant difference between the constants