Question

ou run a regression analysis on a bivariate set of data (n=65n=65). You obtain the regression equation

y=−1.915x+−54.061y=-1.915x+-54.061

with a correlation coefficient of r=−0.626r=-0.626 (which is significant at α=0.01α=0.01). You want to predict what value (on average) for the explanatory variable will give you a value of 30 on the response variable.

What is the predicted explanatory value?
x = _______ 

Answer 1

Answer

We have the regression equation

y = -1.915x -54.061

Now, we have to find the value of x when we have y = 30

so, setting y= 30 in the above equation

so, we get

30 = -1.915x - 54.061

adding 54.061 on each side, we get

30 + 54.061 = -1.915x -54.061 + 54.061............................here -54.061 and +54.061 will become 0

we get

84.061 = -1.915x

dividing both sides by -1.915

we get

(84.061)/(-1.915) = (-1.915x)/(-1.915)..........................here (-1.915)/(-1.915) becomes 1

so, we get

-43.896 = x

So, the required value of explanatory variable x is -43.896