For a sample of eight bears, researchers measured the distances around the bears

Question

For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is

requals=0.846. Using alpha equals=0.05,

determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

Explanation / Answer

Please give a thumbs in case you are content with the answer. Encourages us to answer more questions!

Here' a correlation table significance table.(http://www.nzdl.org/gsdl/collect/hdl/index/assoc/HASH3b4d.dir/t802.png)

At alpha = .05, a .846 correlation is significant. Why?

A sample of 8 bears, means a df = n- 1 = 8-1 = 7

At alpha = .05 has a correlation cutoff of .666 according to the table whose link is shared above

Our correlation is more than that , so it is significant. So, there exists a linear correlation between chest size and weight.

The proportion of the variation that can be explained is known as the R square and can be got by squaring the value of 'r'. r is given out to be 0.846. Hence:

The proportion of the variation in weight can be explained by the linear relationship between weight and chest size is r^2 = .846^2 = 0.716 or 72%

72% the variation in weight can be explained by the linear relationship between weight and chest size

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.