Question

The time it takes a planet to go once around the sun (Length Of Year) depends on its distance from the sun (Distance From Sun). Suppose you wanted to test the claim that this relationship is linear. Assuming you could get data on planets' distances from the sun and the lengths of their years, which of the following would you have to do before deciding whether to proceed with the hypothesis test? Mark all that apply. A. Examine a scatterplot, to see whether there is a linear relationship between the two variables Distance From Sun and Length Of Year. B. Examine a Q-Q plot of the residuals, to see whether the error term (ϵ {"version":"1.1","math":"\epsilon"}) is normally distributed. C. Examine a residual plot, to see whether the variance of the error term is the same for all values of Length Of Year. D. Examine a residual plot, to see whether the variance of the error term is the same for all values of Distance From Sun.

Answer 1

Answer: only one applies and that is (A)

Explanation:

You want to test the claim that the relationship between Length of Year and Distance from Sun is linear.

Since length of year depends on distance from sun, length of year is the dependent variable while distance from sun is the independent variable.

If we wish to express the linear relationship in the form of an equation, we have:

LOY = f(DFS)

That is, Length of year is a function of Distance from sun

Now, if you could get data on both variables, the first thing you should do before deciding whether to proceed with the hypothesis test is:

(A) Examine a scatter plot to see whether there is a linear relationship between the two variables.

A scatter plot is a diagram showing the points where corresponding X and Y values of the given data meet.

Where X is the independent variable and Y is the dependent variable.

After all the points of corresponding X and Y values have been located on the graph, you can draw a line connecting all the points and then another line from the first dot to the last.

If the dots move in a particular direction (e.g. upwards or downwards), there is a linear relationship between the variables.

The hypothesis test to be carried out afterwards (the test to determine whether there is a linear relationship between the variables, in the population) is the TEST OF CORRELATION.

Good luck.