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stiks02 [169]
3 years ago
11

A sample of 100 roller coaters examines the relationship between top speed (response) and max drop (explanatory). Based off of t

he fitted vs residual plot below, select all the assumption have been violated.
The Equal Variance Assumption

There aren’t any outliers.

Both variables are quantitative

The relationship is linear
Mathematics
1 answer:
vekshin13 years ago
6 0

Answer:

From the plot it is clear that assumption 1 and 2 are violated. That is, the assumption of equal variance ( homoscedasticity) and there aren't any outliers.

Step-by-step explanation:

Both variables are quantitative  and The relationship is linear have not been violated.

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I'll abbreviate the definite integral with the notation,

I(f(x),a,b)=\int_a^bf(x)\,\mathrm dx

We're given

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Recall that the definite integral is additive on the interval [a,b], meaning for some c\in[a,b] we have

I(f,a,b)=I(f,a,c)+I(f,c,b)

The definite integral is also linear in the sense that

I(kf+\ell g,a,b)=kIf(a,b)+\ell I(g,a,b)

for some constant scalars k,\ell.

Also, if a\ge b, then

I(f,a,b)=-I(f,b,a)

a. I(2f,1,5)=2I(f,1,5)=2(I(f,1,8)-I(f,5,8))=2(9-4)=\boxed{10}

b. I(f-g,1,8)=I(f,1,8)-I(g,1,8)=9-5=\boxed{4}

c. I(f-g,1,5)=I(f,1,5)-I(g,1,5)=\dfrac{I(2f,1,5)}2-I(g,1,5)=10-3=\boxed{7}

d. I(g-f,5,8)=I(g,5,8)-I(f,5,8)=(I(g,1,8)-I(g,1,5))-I(f,5,8)=(5-3)-4=\boxed{-2}

e. I(7g,5,8)=7I(g,5,8)=7(5-3)=\boxed{14}

f. I(3f,5,1)=3I(f,5,1)=-3I(f,1,5)=-\dfrac32I(2f,1,5)=-\dfrac32(10)=\boxed{-15}

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