Question

a. In your own words, what is meant by the statement that correlation does not imply causality.

b.In your own words, please describe the difference between regression equation y=Bo+B1x and the regression equation ^y=bo+b1x?

Answer 1

a. In your own words, what is meant by the statement that correlation does not imply causality.

"Correlation is not causation" means that just because two things correlate does not necessarily mean that one causes the other.

Correlations between two things can be caused by a third factor that affects both of them.

i.e Correlations between two things can be caused by a third factor that affects both of them.

For example,

Suppose , there is study that people spend more money in shoping and food produxts when it's cold and less when it's hot . So one can find that there is strong relation ship between two variables i.e People spend more money on food and shoppig is cold weather , but in fact it may be beause new year party or christmas eve .

So a more plausible explanation would be that cold weather tends to coincide with festivals and the new year sales .

b.In your own words, please describe the difference between regression equation y=Bo+B1x and the regression equation ^y=bo+b1x?

Here y=Bo+B1x is simple linear regression of dependent variable y on independent variable x .

Here Bo is intercept , which is it is the value of y if the value of x = 0

and   B1 is slope of regression line ,which is the amount that the variable y will change for each 1 unit change in the variable x .

For above y=Bo+B1x

Suppose we estimate values of Bo and B1 ( by least square regresssion method), then we estimate predicted values of y for given values of variable x.

Here predicted value y is denoted by

Now

Regression equation

^y=bo+b1x   or = bo+b1x is sample regression line

You must calculate b0 & b1 to create this line.

Y-hat stands for the predicted value of Y (which was obtained in earlier step by estimating Bo and B1) , and it can be obtained by plugging an individual value of variable x into the equation and calculating y-hat .