Question

For the line = 36.5 + .48x, how do you interpret the value .48?rnrm.gif A. It's the amount of change in y when x increases by one unit.rnrm.gif B. It's the value of y when x = 0.rnrm.gif C. It's the value of x when y = 0.rnrm.gif D. It's the mean of the distribution for the response variable (y) around the explanatory variable (x).rnrm.gif E. It's the amount of change in x when y increases by one unit.

Answer 1

Answer:

A. It's the amount of change in y when x increases by one unit

Step-by-step explanation:

For this case we have the following linear model adjusted:

$\hat y = 36.5 +0.48 x$

Where y is the dependent variable, x the independent variable, 36.5 represent the intercept and 0.48 the slope.

We can analyze one by one the options to select the most appropiate.

A. It's the amount of change in y when x increases by one unit

True, for this case the slope is defined as:

$m =0.48 \frac{\Delta y}{\Delta x}$

And is defined as the amount of change in y when x increase 1 unit.

B. It's the value of y when x = 0

False the value of y when x=0 is y= 36.5+0.48(0) = 36.5

C. It's the value of x when y = 0

False, when y=0 we have this:

$0=36.5 +0.48 x$

$x= -\frac{36.5}{0.48}=-76.04$

D. It's the mean of the distribution for the response variable (y) around the explanatory variable (x)

False, the value 0.48 represent the slope obtained from an estimation of least squares and not represent the mean for the response variable y.

E. It's the amount of change in x when y increases by one unit.

False, is defined inverse as: the amount of change in y when x increase 1 unit.