In 1929 Edwin Hubble investigated the claim that distance ex

In 1929 Edwin Hubble investigated the claim that distance (explanatory, in megaparsecs from Earth) and radial velocity (response, velocity away or towards Earth) of extragalactic nebulae are positively linearly related. Download the data below (Same data, different formats) collected using the Hubble Space Telescope. Use at least 1 decimal place for the following questions.

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a.) Describe the relationship between velocity and distance. The relationship is positive, weak, and linear. The relationship is positive, strong, and linear. The relationship is strong but non-linear. The relationship is negative, strong, and linear. There does not appear to be a relationship between velocity and distance.

b.) What is the regression equation? = + (distance)

c.) What is the estimated mean velocity of objects that are 100 megaparsecs from earth?

d.) Can we use the above regression equation to estimate the mean velocity of objects that are 800 megaparsecs from Earth?

No, that would be extrapolation beyond the range of data we have.

Yes; we can simply substitute 800 into the equation above.

e.) What proportion of variability in radial velocity is explained by distance from Earth?

f.) To test whether distance and radial velocity have a positive linear relationship, which hypotheses would we use?

H0: b = 0 vs. Ha: b > 0.

H0: > 0 vs. Ha: = 0.

H0: b > 0 vs. Ha: b = 0.

H0: = 0 vs. Ha: > 0.

g.) What is the p-value of the hypothesis test above?

h.) What is your conclusion in terms of the problem?

We have weak evidence that there is a positive linear relationship between distance from the earth and radial velocity.

We have no evidence that there is a positive linear relationship between distance from the earth and radial velocity.

We have strong evidence that there is a positive linear relationship between distance from the earth and radial velocity.

We have evidence that there is no linear relationship between distance from the earth and radial velocity.

We have moderate evidence that there is a positive linear relationship between distance from the earth and radial velocity.

Solution

a) The relationship is positive, strong, and linear

b) The regression equation is = 711.7956679 + 67.5361857 (distance)

c) The estimated mean velocity of objects that are 100 megaparsecs from earth is 7465.47

d) Yes; we can simply substitute 800 into the equation above

e) The proportion of variability in radial velocity is explained by distance from Earth is 97.82%

f) H0: = 0 vs. Ha: > 0.

g) The p-value of the hypothesis test is 0

h) We have strong evidence that there is a positive linear relationship between distance from the earth and radial velocity.