Question

In each case state whether you expect the two variables x and y indicated to have positive, negative, or zero correlation.

A. the number x of pages in a book and the age y of the author

B. the number x of pages in a book and the age y of the intended reader

C. the weight x of an automobile and the fuel economy y in miles per gallon

D. the weight x of an automobile and the reading y on its odometer

E. the amount x of a sedative a person took an hour ago and the time y it takes him to respond to a stimulus

Answer 1

Here the concept of dependent, independent variables and correlation have been explained to see the relationship in th e given situations.

Suppose we have a pairs of observations (x, y), (x2, 92), ... (ren, In) The natural question apises that now and y are pelated, Correlation means a mutual relationship or connection between two or more things, i.e. if the value of one variable changes then how does the name of the other vorlable change with respect to it is As 'n value y value There is a t also T tve coppelation As a value ↑ y valie goes on & • There is a -ve coppelation 77 No such coppelation between a and y. Note: Either of the tivo variables, & and y, one has to be the independent variable. and the othor sa dependent voolable (depending on the independent vorlable).

the no. x of pages in a book and the age y of the author Obviously there is zero coprelation or no correlation between the two. The age of the author does not depend on the no. of pages he/she wrote and vice- werya. A very young of 500 a very first young novel author of 500 hy next on white pages and the page Quy B the no.x of pages in a book and the age y of the intended reader It depends. for children (aged 4-10) we see the books are small colourful and thin. Then for teenagers the young adult fictions are of a little more pages ( Noting the above 2 scenarios we can say there might be a tre coppelation. But this is a special case. Generally there is your coppolation as the intended reader woud pead the whole book of any pages) if it interests him/her.

weiant of an automobile (*) and the fuel economy (4) in miles per gallon, The lesser the mass something has the loss energy is required to move it! An automotive terme, the lighter the ean, the less fuel it noeds to move and the better fuel economy it has. 90, if x = weight of an automobile indp. variable = fuel economy in miles per gallon As the value of xle the weight increases the more fuel the automobile lessop the fuel economy . Cre. As XP, Y would need, ie . there is a negative correlation. the weight automobile and the reading Y on its odometer, Odometer is an instrument used measuring the distance travelled for that particular time by a vehicle such as a bieycle or ear. It is attached to the wheel of a vehicle to measure the distanee tpavolled. You can go from place A to place B on youp bleuele op on your cap the distance toavellied would pead the same . There Thero is reno coppelation.

The amount & of a sedative a person took an hour ago and the time it takes him to respond to a stimuly! The more the sedative a penson takes the more it will act upon the nervous system to slow down the body fonetions A sedative affects the brain's natural process by slowing it down, calmness oceurs. Whereas a stimulus is any change in an opganisms environment that Causes the organism to peaet. Obviously then hore time taken to response to stimuli) is dependant on a Camount of sedative taken). If sodative take 1, the more the brain will slow down and hence the time taken to respond to stimuli (7) will also a & There is a positive coppelation,

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