(b) What is the estimated mean velocity of objects that are 1.9 megaparsecs from

Question

(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 2.6 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?

H0: b1 =0 and Ha: b1 < 0H0: b1 = 0 and Ha: b1 0    H0: b1 =0 and Ha: b1 > 0H0: 1 =0 and Ha: 1 < 0H0: 1 = 0 and Ha: 1 0H0: 1 =0 and Ha: 1 > 0

(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.


(g) What would your decision be based on this p-value at the = 0.001 level?

Reject the nullFail to reject the null    

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

The data provides statistical evidence at the = 0.001 level for a positive linear relationship between distance from the earth and radial velocity.The data does not provide statistical evidence at the = 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.

Normal P P Plot of Regression Stanc Scat plot Dependent Variable: The recesson VI Dependent Variable The recesson velocity (in 000 25 .75 100 25 Distance M egaparecs) from earth Regression Standardized Fredlcted Valu Standard t-Value p-Value Regression Table Error 0.6300 Constant 40.784 83.439 0.49 Distance from Earth 454.158 75.237 6.04 0.0001

Explanation / Answer

(a) What is the regression equation?

y= -40.784 + 454.158 x

(b) Estimated mean velocity at x = 1.9 mega parsecs

y = - 40.784 + 454.158 * 1.9 = 822.116

(c)No, because 2.6 is outside the range of the data values for the explanatory variable.

(d) H0: b1 = 0 and Ha: b1 0

these must be hypothesises that slope coefficient is significant or not.

(e)

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

(i)The data is linearly related. YES

(ii) The standard deviations of the response are constant.YES

(iii) The response is normally distributed about the mean function.YES

(f)  What is the p-value of the test? P -- value< 0.0001

(g) What would your decision be based on this p-value at the = 0.001 level?

we will reject the null hypothesis

(h)

What is your conclusion in terms of the problem?

(a) The data provides statistical evidence at the = 0.001 level for a positive linear relationship between distance from the earth and radial velocity. YES

(b) The data does not provide statistical evidence at the = 0.001 level for a positive linear relationship between distance from the earth and radial velocity. NO

(c) The assumptions are not all met, so no conclusion can be made based on the results of this test. NO

Option a is correct.

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