In 1929 Edwin Hubble investigated the claim that distance (explanatory) and radi
ID: 3232396 • Letter: I
Question
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. (a) What is the regression equation? Remember, use 3 decimal places for ALL answers. i_y|x = x (b) What is the estimated mean velocity of objects that are 1.9 megaparsecs from Earth? (c) Can we use the regression equation to estimate the mean velocity of objects that are 26 megaparsecs from earth? Yes, we can estimate the mean velocity of objects that are any distance from earth No, because 2.6 is outside the range of the data values for the explanatory variable. d) If you were to test the claim that there is a positive linear relationship between the explanatory and response variable, what would your null and alternative hypotheses be? H_0: b_1 = 0 and H_0: b_1 0 H_0: beta_1 = 0 and H_a: beta 0 (e) Which of the assumptions for regression appear to be satisfied? Select all that apply. The data a 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. (g) What would your decision be based on this p-value at the a = 0.001 level? Reject the null Fail to reject the null (h) What is your conclusion in terms of the protein? The data provides statistical evidence at the alpha = 0.001 level or a positive linear relationship between distance from the earth and radial velocity. The data does not provide statistical evidence at the alpha = 0.001 level for a positive linear relationship between distance from the earth and radial velocity. The assumptions are not all met, so no conclusion can be made based on the results of this test.Explanation / Answer
d) H0: 1 = 0, Ha: 1 > 0. Hypothesis is always on the population parameter
e) The dependent variable Y has a linear relationship to the independent variable X. To check this, make sure that the XY scatterplot is linear and that the residual plot shows a random pattern.
For each value of X, the probability distribution of Y has the same standard deviation . When this condition is satisfied, the variability of the residuals will be relatively constant across all values of X, which is easily checked in a residual plot.
The Y values are roughly normally distributed (i.e., symmetric and unimodal). A littleskewness is ok if the sample size is large. Normal P-P plot helps for this.
Select all 3
f) p-value = 0.000
g) Reject the null
h) The data provides statistical evidence at the = 0.001 level for a positive linear relationship between distance from the earth and radial velocity.