In 1929 Edwin Hubble investigated the claim that distance ex

In 1929 Edwin Hubble investigated the claim that distance (explanatory) and radial velocity (response) of extragalactic nebulae are positively linearly related. Hubble\'s data is plotted below along with the relevant diagnostic plots. These are the plots and charts needed to analyze data are given below. (Assume all observations are independent) Reference: Hubble, E. (1929) \"A Relationship Between Distance and Radial Velocity among Extra-Galactic Nebulae,\" Proceedings of the National Academy of Science, 168.

The explanatory variable is distance (in megaparsecs) and the response is radial velocity (velocity away or towards the earth). Use 3 decimal places for the following questions.

(e) Which of the assumptions for regression appear to be satisfied? Select all that apply.

The data is linearly related.

The standard deviations of the response are constant.

The response is normally distributed about the mean function.

(f) What is the p-value of the test? Use 3 decimal places.

Solution

e) all 3 assumptions are met, linearity is visible from first scatter plot, normality is visible in the QQ plot (second graph), and constant standard deviation is visible from the third plot.

f) The p-value of regression significance is p-value of slope coefficient, which is less than 0.0001, i.e, ~ 0.000